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Martin Burger07/09/2026, 11:30Plenary Talks
This talk will give an overview of the apperance of phase-separation effects in nonlinear degenerate transpost-cross-diffusion models. Models of this kind can be found
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in a variety of applications from physics over biology to social science. We will provide some examples and discuss the main mechanisms of competion between the degenerate diffusion and group-specific transport properties.... -
Ryan Murray (North Carolina State University)07/09/2026, 14:00Free Boundary Problems in Data Science and Machine Learning
Recent work in machine learning has recognized that many standard algorithms for classification are strongly affected by adversarial attacks. Accordingly, a growing body of research has tried to identify ways to mitigate this issue. This talk will discuss a natural non-parametric formulation of this objective, which can be transformed into a standard classification problem that utilizes a...
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Prof. Weizhu Bao (National University of Singapore)07/09/2026, 14:00Thin Material Structures
In this talk, I will present sharp interface models with anisotropic surface energy for simulating solid-state dewetting and the morphological evolution of patterned islands on a substrate. We will show how to derive the sharp interface model via thermovariation dynamics, i.e. variation of the interfacial energy via an open curve with two triple points moving along a fixed substrate. The sharp...
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Elena Mäder-Baumdicker (Freie Universität Berlin)07/09/2026, 14:00Geometric Flows and Evolving Free Boundaries
The area preserving curve shortening flow with Neumann free boundary conditions shortens a curve that is attached perpendicularly to a bounded domain $\Omega$ in the plane but keeps the enclosed area fixed. The end points of that curve move in the boundary curve of $\Omega$. Its limits are candidates for minimizers for the relative isoperimetric problem in the plane (thus, they are circular...
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Yifei Li (Tuebingen University)07/09/2026, 14:30Thin Material Structures
In this talk, we present a numerical analysis of the Eyles-King-Styles tumor growth model, a free boundary problem coupling a Poisson equation in the bulk \Omega with a forced mean curvature flow on its boundary \Gamma. Unlike existing evolving surface analyses based on integer-order Sobolev spaces, this bulk-surface coupling requires H^{1/2}-order regularity on \Gamma. We establish a...
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José A. Iglesias (University of Twente)07/09/2026, 14:30Free Boundary Problems in Data Science and Machine Learning
We focus on decomposability and extremality properties of nonlocal perimeters. Two archetypal types of these are the Gagliardo perimeter based on the eponymous seminorms and the nonlocal distributional Caccioppoli perimeter, both which can be considered with with finite and infinite interaction ranges.
A nonlocal notion of indecomposability associated to these perimeters is introduced, and...
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Saša Lukić (RWTH Aachen University)07/09/2026, 14:30Geometric Flows and Evolving Free Boundaries
In this talk, we discuss up to two different aspects of the two-phase Mullins--Sekerka evolution.
In the first part, we investigate the convergence to equilibrium configurations: It is well-known that nearly spherical interfaces given as nearly radial graphs over spheres converge to an equilibrium configuration exponentially fast with a rate $\sim 1/R^3$, where $R$ is the radius of the...
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Marco Salvalaglio (TU Dresden)07/09/2026, 15:00Thin Material Structures
Solid-state dewetting is the process through which thin solid films break and retract on a substrate, leading to the formation of nanostructures. Dewetting in single-crystalline films is well understood as a surface-energy-driven phenomenon governed by surface diffusion. Polycrystalline films, by contrast, exhibit additional complexity due to the presence of extended defects (grain boundaries)...
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Andrea Poiatti (University of Parma)07/09/2026, 15:00Geometric Flows and Evolving Free Boundaries
In this talk, I would like to introduce a novel weak solution concept for two-phase Volume Preserving Mean Curvature Flow, having both properties of unconditional global-in-time existence and weak-strong uniqueness. These solutions consist in evolving varifolds coupled with the phase volumes by a transport equation. We preliminarily concentrate on the existence, showing first that any sharp...
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Prof. Buyang Li (The Hong Kong Polytechnic University)07/09/2026, 15:30Thin Material Structures
Finite element methods and kinematically coupled schemes that decouple the fluid velocity and structure displacement have been extensively studied for incompressible fluid-structure interaction (FSI) over the past decade. While these methods are known to be stable and easy to implement, optimal error analysis has remained challenging. Previous work has primarily relied on the classical...
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Jonas Ingmanns (Institute of Science and Technology Austria)07/09/2026, 15:30Geometric Flows and Evolving Free Boundaries
Consider the evolution of sets by forced mean curvature flow through a field of random obstacles. The effective large scale behaviour is expected to be a first order motion. However, previous results heavily relied on the assumption that there is a global minimum speed of expansion and hence on the absence of any actual obstacles.
We obtain a quantitative homogenization result even with...
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Prof. Maria Giovanna Mora (Università di Pavia)07/09/2026, 16:30Plenary Talks
Nonlocal interaction energies play a central role in describing the collective behavior of large particle systems in a wide range of applications. In this lecture we will focus on interactions that are short-range repulsive and long-range attractive. We will review the key results on the existence and uniqueness of minimizers, and present their explicit characterization in the classical case...
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José Francisco Rodrigues (Universidade de Lisboa)07/09/2026, 18:00Plenary Talks
The interdisciplinary field of free-boundary problems – that is, problems arising in a wide variety of phenomena in nature, science and technology where the boundaries delimiting the domains are not known a priori and constitute unknowns to be determined – saw remarkable developments in their mathematical treatment during the last half a century.
Seeking to contextualise this class of...
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Prof. Julian Fischer08/09/2026, 09:00Plenary Talks
The relative energy/entropy method has been a powerful tool for establishing (weak-strong) uniqueness, stability, and singular limits in continuum mechanics ever since its inception in the 70s by Dafermos and DiPerna. However, its application to interface evolution problems has faced a major obstacle in the form of the lack of strict convexity of the interface area functional. Recently, it has...
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Maria Stella Gelli (Università di Pisa Dipartimento di Matematica)08/09/2026, 10:30Free Boundaries in Shape Optimization
Starting from 2D lattice spin configurations satisfying the uniform state $\mathbf{e}_3$ outside a bounded domain $\Omega$, we investigate atomistic energies consisting of an exchange Heisenberg term together with an interfacial Dzyaloshinskii--Moriya interaction (DMI). In both discrete and continuum settings, imposing spatial confinement along with a topological constraint ($\text{degree}=1$)...
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Riccardo Cristoferi08/09/2026, 10:30Free Boundary Problems in Data Science and Machine Learning
The analysis of Big Data is one of the most important challenges of the modern era. A first step in order to extract some information from a set of data is to partition it according to some notion of similarity. When only geometric features are used to define such a notion of similarity and no a priori knowledge of the data is available, we refer to it as the clustering problem.
Typically...
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Maik Porrmann (Dresden University of Technology)08/09/2026, 10:30Thin Material Structures
We propose a numerical method for fluid deformable surfaces governed by surface Stokes flow and Helfrich bending energy under active growth, aiming to model shape evolution of the epithelium sheets in developmental processes. As a new extension of the model, we prevent self-intersections, which commonly arise under large deformations or low enclosed volume to area ratios, by incorporating the...
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Prof. Helmut Abels (Universität Regensburg)08/09/2026, 10:30Phase Field Methods in Real-World Applications
We consider the linearized system for the sharp interface limit of a Navier-Stokes/Allen-Cahn system around a suitable approximate solution.
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With the aid of a suitable weight taking the distance to the interface and the interfacial thickness into account we obtain optimal regularity estimates, which are uniformy in the interfacial thickness. This enables to improve previous convergence... -
Shokhrukh Kholmatov (University of Vienna)08/09/2026, 11:00Free Boundaries in Shape Optimization
We discuss regularity properties of Cartesian minimizers of the (anisotropic) area functional
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[
\int_a^b \Phi(-Du,1),dx+\int_a^b |u-g|^p,dx
]
defined on (BV(a,b)). We prove that if the (L^\infty)-norm of the forcing term (g) is sufficiently small, then every minimizer is locally Lipschitz continuous. Moreover, if the anisotropy (\Phi) is smooth and uniformly elliptic, then every minimizer... -
Fan Cheng (Freie Universität Berlin)08/09/2026, 11:00Phase Field Methods in Real-World Applications
We study the homogenisation of an incompressible viscoelastoplastic fluid in randomly perforated domains. The mesoscopic model couples the balance of momentum with the evolution of a deviatoric internal stress tensor. The latter is transported by the flow through the Zaremba–Jaumann derivative and is subject to a non-smooth plastic dissipation law as well as stress diffusion. This model is...
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Enno Igel (TU Dresden)08/09/2026, 11:00Thin Material Structures
We consider the surface Stokes-Helfrich problem using a stream function formulation. The formulation is considered for simply connected surfaces without boundary. It is based on a splitting of the velocity field in normal and tangential components and the Helmholtz decomposition of the tangential part. For its numerical solution the surface is approximated by higher order isoparametric...
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Eloi Martinet (JMU Würzburg)08/09/2026, 11:00Free Boundary Problems in Data Science and Machine Learning
We propose a single-layer neural parametrization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks explicitly represent both the support and gauge functions of a convex body. We prove a universal approximation theorem for convex sets under this parametrization. Empirically, we demonstrate the method on shape optimization and inverse design tasks,...
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Cyrill Muratov (University of Pisa)08/09/2026, 11:30Free Boundaries in Shape Optimization
In this talk I will present our treatment of a geometric variational
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problem arising from modeling the equilibrium shapes of liquid drops
whose energy presents a competition of surface tension with the
repulsive Coulombic energy of a fixed number of point charges inside
the drop. The continuum analog of this problem in which the liquid is
treated as a perfect conductor is known to be... -
Simon Masnou (Université Lyon 1)08/09/2026, 11:30Free Boundary Problems in Data Science and Machine Learning
The talk will focus on neural operators with few parameters for approximating the Willmore flow of oriented or non-oriented interfaces in space dimensions 2 and 3.
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The proposed neural networks are trained on implicit representations of interfaces evolving by Willmore flow.
Various numerical simulations will be presented, together with applications to curve and surface reconstruction from... -
Jonas Stange (Universität Regensburg)08/09/2026, 11:30Phase Field Methods in Real-World Applications
We consider a general class of convective bulk-surface Cahn-Hilliard systems with singular potentials. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn-Hilliard-type allow for dynamic changes of the contact angle between the diffuse interface and the boundary as well as absorption of material by the boundary. In this talk, I present recent results...
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Albert Chern (University of California San Diego)08/09/2026, 11:30Thin Material Structures
Scalar vorticity formulation for fluid equations on surfaces is computationally attractive. However, the vorticity equation is incomplete on a non-simply-connected surface. We derive a new evolution equation for the finite dimensional harmonic (cohomology) components of the flow. We also show that the vorticity equation has a curvature-dependent, vorticity production term in addition to the...
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Yadong Liu (Nanjing Normal University)08/09/2026, 12:00Phase Field Methods in Real-World Applications
In this talk, I will report a recent work on a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum mixture theory. It adopts a mass-averaged (barycentric) velocity so that the two-phase flow is quasi-incompressible: the...
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Samuel Weidemaier08/09/2026, 12:00Free Boundary Problems in Data Science and Machine Learning
We present a variational neural approach for computing global signed distance functions (SDFs) from unoriented point clouds, focusing on the medial axis as the unknown jump set of the SDF gradient. The method is based on the observation that the SDF gradient is smooth away from the medial axis, but jumps where the nearest-point projection onto the surface is not well-defined. We formulate SDF...
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berardo ruffini (Università di Bologna)08/09/2026, 12:00Free Boundaries in Shape Optimization
We introduce a class of shape optimization problems modeled on Hartree type energies. From a shape optimization point of view, the energy is a sort of lower order perturbation of the first Dirichlet eigenvalue energy. We will partially discuss the existence and rigidity of optimizer in certain regimes and focus on the nonexistence issue in other regimes. The short talk is based on ongoing...
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20. Surface Beris-Edwards-Helfrich models - how local orientational order can influence global shapeAxel Voigt08/09/2026, 12:00Thin Material Structures
We consider general models for hydrodynamic surface liquid crystals on (self-)evolving surfaces. We focus on nematic liquid crystals and model them using a Q-tensor approach. The model will be derived using the Lagrange-d´Alambert principle. Our Q-tensor is a 3D object defined on the surface. Here we address specific forms, essentially "surface conforming" Q-tensors, with eigenvectors in...
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Robert Lasarzik (WIAS)08/09/2026, 14:00Phase Transitions and Pattern Formation
In this talk, we consider an Allen—Cahn system with the obstacle potential that guarantees mass conservation. This equation is coupled to two linear elasticity equations and a nonlocal operator. This system emerged from an algorithm for a problem in two-scale topology optimization using the phase-field approach. We prove the existence of weak solutions for the associated inclusion and comment...
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Qi Wang (U of South Carolina)08/09/2026, 14:00Free Boundaries in Active Matter
We propose several linear, fully decoupled numerical schemes with first- and second-order temporal accuracy for a novel Q-tensor-based two-phase hydrodynamic model that describes the coupling of active nematic liquid crystal solutions with isotropic solid substrates. The model is derived from the generalized Onsager principle and includes nontrivial terms that contribute zero to the total free...
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Hans Knüpfer (University of Heidelberg)08/09/2026, 14:00Domain Walls and Patterns in Local and Non-local Geometric Variational Problems
We study the existence and structure of one-dimensional 360 degree walls in thin uniaxial ferromagnetic films. These structures are topological defects which consist of two oppositely charged 180 degree walls interacting by nonlocal stray-field energy. We show existence for nonzero wall angles when the stray-field interaction is sufficiently weak, while at zero angle no minimizer exists. We...
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Scott Weady (Flatiron Institute)08/09/2026, 14:30Free Boundaries in Active Matter
We develop and analyze a model for a flat microbial droplet growing on the surface of a viscous fluid. The model describes growth-induced stresses at the fluid surface, density variations in the bulk due to nutrient consumption, and the resulting fluid flows that arise. We reformulate this free boundary problem as a system of integro-differential equations defined solely on the microbial...
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Chiara Leone (University of Naples Federico II)08/09/2026, 14:30Domain Walls and Patterns in Local and Non-local Geometric Variational Problems
Optimal local Lipschitz regularity for scalar almost minimizers of Alt-Caffarelli-type functionals
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$$ \mathcal{F}({v}; \Omega) = \int_\Omega \varphi(x,\left|\nabla v(x) \right|)+ \lambda \chi_{\{{v}>0\}} (x) \,dx, $$ with growth function $\varphi$ a generalized Orlicz function, is established.
The results presented in this talk have been obtained in collaboration with Giovanni Scilla... -
Luca Scarpa (Politecnico di Milano)08/09/2026, 14:30Phase Transitions and Pattern Formation
We propose a stochastic Cahn--Hilliard model driven by transport noise in order to describe phase-separation phenomena occurring in mixtures of
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turbulent fluids. The model is analysed in its thermodynamically-relevant framework, namely employing a singular Flory--Huggins potential and a possibly degenerate mobility, and the noise is considered both in It\^o and Stratonovich form. As a... -
Stefan Metzger (Friedrich-Alexander-Universität Erlangen-Nürnberg)08/09/2026, 15:00Phase Transitions and Pattern Formation
The Cahn-Hilliard equation is a deterministic model for the description of phase separation processes in metal alloys, which occur if the alloy is rapidly cooled below a critical temperature. This equation can be interpreted as an $H^{-1}$-gradient flow of the Ginzburg-Landau energy functional, which consists of a gradient term and double-well potential favoring phase separation. If the quench...
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Dr Ingo Nitschke (TU Dresden - Institute of Scientific Computing)08/09/2026, 15:00Free Boundaries in Active Matter
Many mathematical models for active interfaces, biological membranes, and other free boundary problems combine geometric evolution with conserved quantities living on evolving surfaces. This motivates the development of general variational frameworks for deriving energy-dissipative evolution equations.
In this talk, we present a general variational framework for constructing coupled...
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Robert Nürnberg08/09/2026, 15:30Phase Transitions and Pattern Formation
We consider a phase field model for crystal growth on a curved surface.
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A particular emphasis must be placed on the choice of the anisotropic
energy density functional. We advocate for a construction that is based on
fixing a density on the tangent space of a chosen point on the surface,
and then moving it along geodesics to the other tangent spaces.
We propose a surface finite element... -
Theresa Simon (University of Münster)08/09/2026, 15:30Domain Walls and Patterns in Local and Non-local Geometric Variational Problems
In the radial setting, we analyze how magnetic skyrmions transition to (large scale) bubbles in the entire regime of positive energetic cost of domain walls, i.e., far away from the conformal limit. First, we demonstrate existence of radial, skyrmionic bubbles throughout this maximal regime of energetic feasibility. Second, we perform a Gamma-convergence analysis in the limit of vanishing...
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Oleksii Krupchytskyi (The Pennsylvania State University)08/09/2026, 15:30Free Boundaries in Active Matter
We begin with a brief overview of the rapidly developing research area of active matter, a.k.a. active materials. These materials are intrinsically out of equilibrium resulting in novel physical properties whose modeling requires the development of new mathematical tools. We present a free boundary PDE model a cytoskeleton of a moving cell. The key mathematical features of our model are the...
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Michael Eden (University of Regensburg)08/09/2026, 16:30Contributed Talks
We consider a coupled Stokes–reaction–diffusion system posed in a non-periodically perforated domain with solid spherical inclusions whose radii evolve according to a surface reaction law. In the critical scaling regime, where the inclusions have size of order (\e^3), we prove well-posedness of the microscopic problem using a contraction mapping argument. We then analyze the asymptotic...
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Shawn Walker (Louisiana State University)08/09/2026, 16:30Numerical Methods for Geometric PDEs
We present a framework for computing shape derivatives of boundary functionals discretized with unfitted finite element methods. The main idea is to replace the boundary functional by a narrow-band volumetric regularization prior to discretization. This yields an exact Fr'echet derivative of the resulting discrete functional with respect to the discrete level set function, without any...
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Jürgen Sprekels (Weierstrass Institute, Anton-Wilhelm-Amo-Strasse 39, 10117 Berlin, Germany)08/09/2026, 16:30Phase Field Methods in Real-World Applications
In this talk, we study the optimal control of a phase field system of viscous Cahn-Hilliard type modeling tumor growth, in which a hyperbolic relaxation of the chemical potential is added to the equation governing the phase evolution. In addition to well-posedness results for the state system, we analyze the differentiability properties of the associated control-to-state operator and derive...
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Luca Briani (Technische Universität München)08/09/2026, 16:30Free Boundaries in Shape Optimization
We present a variational definition of the essential spectrum suitable for nonlinear operators such as the Dirichlet p-Laplacian and discuss an extension of Persson's theorem to this framework. Finally, we show that the Ljusternik-Schnirelmann minmax levels of the constrained p-Dirichlet integral are attained whenever one of these levels is below Persson's threshold. This is based on joint...
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Evan Gawlik (Santa Clara University)08/09/2026, 17:00Numerical Methods for Geometric PDEs
If a simplicial triangulation is equipped with a piecewise smooth Riemannian metric that has single-valued tangential-tangential components on element interfaces, then there are various notions of curvature that one can define, even though the classical formulas for curvature involving derivatives of the metric no longer make sense. In this talk, I will explain the origins of these...
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Maria del Mar Gonzalez Nogueras (Universidad Autonoma de Madrid)08/09/2026, 17:00Free Boundaries in Shape Optimization
Motivated by the study of the Paneitz operator in geometry, we consider eigenvalue problems for some fourth-order problems, with a particular emphasis on eigenvalue bounds and shape optimization.
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Lauro Silini08/09/2026, 17:00Contributed Talks
Self-similar shrinkers describe generic singularities of multiphase mean curvature flow at the parabolic scale. The classification of stable self-shrinkers, conjectured by Ilmanen, is a central step towards understanding global dynamics of generic flows. While the compact case of the circle is well understood at this point, classification of stable, non-compact shrinkers remains still...
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Monica Conti08/09/2026, 17:00Phase Field Methods in Real-World Applications
In this talk, we consider a class of Cahn–Hilliard equations with nonlinear diffusion, arising in the description of complex materials.
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We discuss recent results on existence, regularization, stability, and convergence to equilibrium under very general assumptions. In particular, we show that the strong convexity assumption on the interfacial energy, which underlies much of the existing... -
Abramo Agosti (University of Pavia)08/09/2026, 17:30Phase Field Methods in Real-World Applications
In this talk I will present new results about the Active Cahn-Hilliard equation, which is a variant of the Cahn-Hilliard equation not derivable from variational principles which describes active materials constituted by particles that can convert energy into directed motion. This model has multiple applications in biomedicine and engineering. I will show quantitative results about the...
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Yakov Berchenko-Kogan (Florida Institute of Technology)08/09/2026, 17:30Numerical Methods for Geometric PDEs
Blow-up finite elements, developed jointly with Evan Gawlik, were motivated by a vexing problem when discretizing tangent vector fields on surfaces: For a discretized surface, the angles at vertices generally no longer sum to 360 degrees. As a result, it is not possible to construct a vector field approximation that is continuous within each element, tangent to the surface, and continuous...
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Mickaël Nahon (Université Grenoble Alpes)08/09/2026, 17:30Free Boundaries in Shape Optimization
Consider the following functional
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$$u\in H^2(D,\mathbb{R})\mapsto\int_D(|\nabla^2 u|^2+\chi_{u\neq 0})$$ where $D\subset \mathbb{R}^2$. This is a higher order analogue of the Alt-Caffarelli problem, and its local minimizers are linked to several shape optimization question: primarily with the minimization (under area constraint) of the critical buckling load of a clamped plate... -
Nicolas Van Goethem (Universidade de Lisboa)08/09/2026, 18:00Free Boundaries in Shape Optimization
We propose a mechanism for the onset of polygonization in crystals with dislocations. Starting from a diffuse distribution, we show that the interaction between elasticity and dislocation motion can destabilize the homogeneous state. The classical Peach–Koehler force tends to stabilize this state, while a non-local Beltrami contribution drives the instability.
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The fastest-growing structures... -
RICCARDA ROSSI (Università degli studi di Brescia)08/09/2026, 18:00Phase Field Methods in Real-World Applications
Several phase-field models have the underlying structure of
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generalized gradient systems in Banach spaces, whose evolutions
are generated by the interplay between an energy functional
and a dissipation potential. We focus on the case in which the dual
dissipation potential is given by a sum of two functionals and show
that solutions of the associated gradient-flow evolution... -
Erica Ipocoana (Freie Universität Berlin)08/09/2026, 18:30Phase Field Methods in Real-World Applications
We introduce an isothermal phase-field model for the coupled evaporation and crystallization of an aerosol droplet containing dissolved solutes: as the liquid evaporates, the dissolved solute, for example salt, becomes increasingly concentrated and, once it exceeds a saturation threshold, precipitates by forming a crystalline phase.
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The model is described by a three-phase (liquid,... -
JOAQUIM SERRA (ETH ZURICH)09/09/2026, 09:00Plenary Talks
In many nonconvex variational free-boundary problems, regularity theory has traditionally focused on energy minimizers. Yet stable—and, more generally, finite-index—critical points arise naturally in physical models and geometric variational constructions, and are often just as relevant. A basic question is therefore: how much of the regularity theory for minimizing free boundaries survives...
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Malte Kampschulte (Charles University Prague)09/09/2026, 10:30Contributed Talks
Consider the coupled system of rigid particles flowing inside a Navier-Stokes fluid. If one sends the number of particles to infinity while at the same time shrinking their size, then at the right scaling the expected limit is the Navier-Stokes-Vlasov system. Turning this formal limit into a rigorous proof however is still an open problem. The aim of this talk is to present some partial...
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Paola Pozzi09/09/2026, 10:30Numerical Methods for Geometric PDEs
In this talk we discuss the question of finding a network configuration of minimal length connecting three given points in the Heisenberg group.
After formulating a suitable horizontal curve shortening flow, we present numerical experiments based on a stable fully discrete finite element scheme that provide useful insights into the rich landscape of this sub-Riemannian geometry.
This...
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Ulisse Stefanelli (Unviersity of Vienna)09/09/2026, 10:30Phase Transitions and Pattern Formation
Accretive growth is a fundamental mechanism in biological, natural, and technological systems. I will present two phase-field models for finite-strain viscoelastic solids undergoing mechanically driven accretion, addressing both phase-transition dynamics and the build-up of growth-induced incompatibilities.
The first model describes a two-phase viscoelastic medium in which one phase...
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Dieter Bothe09/09/2026, 10:30Hydrodynamic Models with Moving Contact Lines
Dynamic wetting poses a fundamental modeling challenge because the motion of a material contact line requires slip at the solid wall and a consistent coupling between contact-line kinematics, wall stresses, and the dynamic contact angle. After briefly reviewing these modeling constraints, we present the contact-region generalized Navier boundary condition (CR-GNBC). The model replaces the...
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Nils Bullerjahn09/09/2026, 11:00Phase Transitions and Pattern Formation
In this talk we analyse a bulk--surface finite element in space and backward difference in time full discretization of a general two-parameter family of Cahn--Hilliard equations with dynamic boundary conditions. A novel proof strategy using discrete almost mass conservation and a suitable Poincaré–Wirtinger inequality is presented to achieve optimal-order fully discrete error estimates in the...
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Christina Lienstromberg (University of Stuttgart)09/09/2026, 11:00Hydrodynamic Models with Moving Contact Lines
We study the dynamic behaviour of a thin viscous fluid film coating the inner wall of a rotating cylinder -- a so-called rimming flow.
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The resulting equation for the height of the fluid film is a quasilinear, degenerate parabolic PDE of fourth order.
Various competing effects drive the dynamics of the interface -- viscosity, surface tension and gravity.
For a positive surface tension... -
Mr Nishant Ranwan (PhD scholar at School of Mathematics, IISER Thiruvananthapuram)09/09/2026, 11:00Contributed Talks
This talk presents the study on the finite element approximation of a fluid–structure interaction (FSI) problem. The FSI problem is governed by the incompressible Navier–Stokes equations and the equations of linear elasticity.
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We consider that both the fluid and solid subdomains are stationary. We incorporate the grad-div stabilization for the fluid part during the spatial discretization. In... -
Carolin Mehlmann09/09/2026, 11:30Numerical Methods for Geometric PDEs
Nonconforming surface finite elements have recently been developed to discretize 3D vector-valued compressible flow problems arising in climate modeling. In this talk, we present an error analysis of this approach for a vector-valued Laplace problem, a key operator in fluid equations on surfaces. The problem is discretized via edge-integration on local flat triangles using the nonconforming...
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Moritz Gau (WIAS Berlin)09/09/2026, 11:30Phase Transitions and Pattern Formation
Viscoelastic phase separation occurs in binary fluids where the constituent molecules aggregate on strongly different time scales. Typically, the morphology of this process features volume shrinking, sponge-like structures and phase inversion. Such phenomena are observed in polymer solutions, for instance, where polymer chains are much larger and migrate much more slowly compared to solvent...
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Pierre Marie Ngougoue (University of Duisburg-Essen)09/09/2026, 11:30Contributed Talks
The interaction of a three-dimensional barotropic compressible fluid with a viscoelastic shell occupying part of the fluid boundary is considered. Local-in-time existence and uniqueness of strong solutions are established in a fully Eulerian framework based on a localised Hanzawa transform. In addition, blow-up criteria are derived, providing sufficient conditions for extending strong...
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Georgy Kitavtsev (Middle East Technical University, Nothern Cyprus Campus)09/09/2026, 12:00Hydrodynamic Models with Moving Contact Lines
In this talk, we consider the nonlinear system of coupled degenerate PDEs describing evolution of the free surface of a viscous thin liquid sheet. We show that in the associated Lagrangian coordinates the system transforms to the singular diffusion porous medium type equation equipped with the non-homogeneous in space and time source term having zero mean.
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In the regime of vanishing sheet... -
Songzhuang Chen09/09/2026, 12:00Phase Transitions and Pattern Formation
We establish the local well-posedness of strong solutions for a thermodynamically consistent diffuse interface model describing two-phase flows with surfactants, specifically the so-called Model C introduced by Garcke, Lam, and Stinner. The highly non-standard, mixed-order strongly coupled structure of Model C invalidates the classical Agmon-Douglis-Nirenberg theory and conventional...
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Mario Bukal (University of Zagreb Faculty of Electrical Engineering and Computing)09/09/2026, 12:00Contributed Talks
Motivated by the problem of rigorously justifying reduced elastohydrodynamic models, which are commonly used in microfluidics, we study a fluid–plate interaction system and identify conditions guaranteeing uniform separation of the elastic plate from the opposing rigid boundary.
More precisely, we consider a three-dimensional incompressible viscous fluid governed by the Navier–Stokes...
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Dennis Trautwein (Universität Regensburg)09/09/2026, 12:00Numerical Methods for Geometric PDEs
The numerical simulation of viscoelastic two-phase flows involves complex free boundary dynamics and faces major challenges, such as the High Weissenberg Number Problem and the loss of positive definiteness of the conformation tensor.
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In this presentation, we introduce an energy-stable numerical framework designed to address these issues. First, we discuss energy-stable, positivity-preserving... -
Dr Konstantinos Bessas (University of Pavia)09/09/2026, 14:00Contributed Talks
We establish a pointwise limit theorem for a broad class of parameter-dependent BMO-type seminorms as the parameter tends to zero. By introducing novel BMO-type seminorms, we provide a unified framework that extends several existing results and yields derivative-free characterizations of Sobolev-type spaces, both in the scalar and in the vector-valued setting.
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More precisely, for any open set... -
Charles Elbar (Université Claude Bernard Lyon 1)09/09/2026, 14:00Phase Transitions and Pattern Formation
We consider a simplified model for tumor growth: a Cahn-Hillard equation with a repulsive potential, that models the pressure inside the tissue. This potential is of the form u^{\gamma}. In the so-called incompressible limit when gamma is sent to infinity, we observe that the pressure admits a jump at the free boundary of the model. This is a joint work with Benoît Perthame and Jakub Skrzeczkowski.
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Dmitry Golovaty09/09/2026, 14:00Free Boundaries in Active Matter
I will discuss pattern formation in active matter confined to a thin film of microtubules activated by Adenosine Triphosphate (ATP), focusing on configurations corresponding to high anisotropy of the elastic constants. This is the result of the joint work with M. Carme Calderer (Minnesota), Jordi Ignes-Mullol (Barcelona), Francesc Sagues (Barcelona), Lingxing Yao (Akron), and Longhua Zhao...
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Yuchuan Yang (University of Michigan)09/09/2026, 14:30Hydrodynamic Models with Moving Contact Lines
In recent years, newly available experimental measurements of grain boundary motion in polycrystalline materials challenge the assumption of the Herring angle condition at triple junctions (a well-known force balance condition). One of the proposed explanations for the discrepancy between these experimental data and the traditional model is the presence of triple junction drag. In this talk, I...
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Timothy Atherton (Tufts University)09/09/2026, 14:30Free Boundaries in Active Matter
Liquid crystals provide remarkable examples of two-way coupling between internal order and geometry: orientational or layered order responds to confinement and interfaces, while the resulting elastic stresses can reshape the domain itself. I will discuss recent variational and computational work on this coupling in nematic and smectic systems. In nematic droplets, simultaneous optimization of...
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Amjad Saef09/09/2026, 14:30Contributed Talks
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a phase-field. We investigate both the case of an independently evolving phase-field and of coupled phase-field evolution driven by a viscous Hamilton-Jacobi...
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Andrea Poiatti (University of Parma)09/09/2026, 15:00Phase Transitions and Pattern Formation
I will discuss the initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular potential, showing that any weak solution converges to a single equilibrium under minimal assumptions, i.e., the existence of a global weak solution satisfying an energy inequality. This result also holds in the three-dimensional case, which was an open problem so far...
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Manisha Chowdhury (Otto-von-Guericke-University Magdeburg)09/09/2026, 15:00Contributed Talks
Surface flow problems have attracted considerable attention in recent years because of their broad applications in science and engineering. In this talk, we investigate the numerical approximation of the surface Stokes equations posed on a two-dimensional manifold embedded in three-dimensional space. The surface velocity is discretized using the nonconforming Crouzeix–Raviart finite element,...
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Slobodan Zumer (University of Ljubljana, Faculty of Mathematics and Physics)09/09/2026, 15:00Free Boundaries in Active Matter
Topological active soft matter includes fluids characterized by orientational ordering of constituting entities, ranging from anisotropic particles that extract energy from their surroundings to biological and living systems that convert chemical energy. Due to its softness, topological soft matter rarely exhibits homogeneous orientational order. Most of the frustration arising from the...
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Benjamin Gess (TU Berlin & MPI MiS Leipzig)09/09/2026, 15:00Hydrodynamic Models with Moving Contact Lines
We begin by informally demonstrating how the gradient flow structure of the deterministic thin film equation, which encodes the balance between driving capillary forces and limiting viscous forces, can be used as a foundation for the thermodynamically consistent introduction of fluctuations. This approach is then pursued at the level of a spatial discretization of the gradient flow structure,...
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Robert Nürnberg09/09/2026, 15:30Hydrodynamic Models with Moving Contact Lines
We present and analyze a variational front-tracking method for a sharp-interface model of multiphase flow. The fluid interfaces between different phases are represented by curve networks in two space dimensions (2d) or surface clusters in three space dimensions (3d) with triple junctions where three interfaces meet, and boundary points/lines where an interface meets a fixed planar boundary....
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Yadong Liu (Nanjing Normal University)09/09/2026, 15:30Phase Transitions and Pattern Formation
In this talk, I will report a recent work on the sharp interface limit of a Navier--Stokes/Allen--Cahn system as the interfacial thickness $\varepsilon$ tends to zero for well-prepared initial data as long as the limit system possesses a sufficiently smooth solution. We propose a systematic argument based on the linearization of the errors. The convergence results relies crucially on uniform...
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Giacomo Colombo (ETH Zürich)09/09/2026, 15:30
The Stefan problem describes the evolution of phase transitions, such as ice melting into water. In this talk, we will discuss the fine structure of the singular set of the free boundary. More precisely, we recently proved that, outside an $(n-2)$-dimensional set, the singular part is contained in an $(n-1)$-dimensional manifold of class $C^\infty$. We will first describe this result and...
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Matteo Novaga (University of Pisa)09/09/2026, 16:30Plenary Talks
The classical Kelvin problem seeks the optimal equal-volume partition of $\mathbb R^d$ minimizing boundary surface area. In this talk, we present recent progress on periodic minimizing partitions in both isotropic and anisotropic settings.
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Focusing first on two-dimensional configurations, we analyze optimal planar tilings and extend these techniques to higher dimensions, exploring... -
Senjo Shimizu (Kyoto University)10/09/2026, 09:00Plenary Talks
A time-dependent free surface problem for the Navier-Stokes equations which describes the motion of viscous fluid in a domain close to the half-space is considered. We discuss well-posedness of the problem for an initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space. Utilizing the almost...
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Ulisse Stefanelli (Unviersity of Vienna)10/09/2026, 10:30Phase Field Methods in Real-World Applications
I will present some existence result for a mathematical model of accretive growth in confined environments. Accretive growth occurs ubiquitously in most biological systems, as well as in many natural and technological ones. The model describes the growth process through a level-set formulation, leading to a free-boundary problem combined with a stationary Hamilton-Jacobi equation in a...
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Mark Allen (Brigham Young University)10/09/2026, 10:30Degenerate PDEs and Free Boundary Problems
We will discuss a parabolic PDE that arises in models for combustion and wildfire. Our main concern is the fire front: how it moves and what shape it can take. In the study of PDEs, the fire front is the free boundary. In this problem, at a fixed time the shape of the fire front can have singularities. However, when the fire front is viewed as a free boundary in space-time, we show that the...
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Boris Muha (University of Zagreb Faculty of Science)10/09/2026, 10:30Fluid-structure Interactions
We consider the abstract evolution problem $u'(t)=Au(t)+f(t)$ in a
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Hilbert space, where $A$ generates a strongly stable but not uniformly
stable $C_0$-semigroup $S(t)$, the typical situation for partially
dissipative systems such as coupled heat--wave models, which arise as
simplifications of fluid--structure interaction. In this setting
classical resonance, i.e.\ an eigenvalue of $A$ on... -
Dennis Trautwein (Universität Regensburg)10/09/2026, 11:00Phase Field Methods in Real-World Applications
In this talk, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a Cahn--Hilliard-type equation with cross diffusion for the relative chemical concentration of one lipid phase, coupled to a fourth-order reaction-diffusion...
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Krutika Tawri (University of Washington)10/09/2026, 11:00Fluid-structure Interactions
In this talk, we will consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, elastodynamics of which is modeled by 1D plate equations. The fluid and the structure are nonlinearly coupled at the fluid-structure interface. The fluid flow is driven by dynamic pressure data...
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Hector Chang-Lara (Universidade de Coimbra and CIMAT)10/09/2026, 11:00Degenerate PDEs and Free Boundary Problems
Many equations arising in mathematics and the sciences have a remarkable smoothing effect. The heat equation provides a striking example: even when starting from very irregular initial data, its solutions become smooth instantaneously. Classical regularity theory seeks to explain this phenomenon for broad classes of elliptic and parabolic equations. In many important problems, however, the...
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José Francisco Rodrigues (Universidade de Lisboa)10/09/2026, 11:30Optimization and Free Boundaries
In the classical obstacle problem, the corresponding optimal control of the variational inequality concerns usually its solution, i.e. the minimal supersolution of a Poisson equation lying above the obstacle, which is the control together with the external force. In this work we discuss the control of the free boundary in terms of different frameworks of the characteristic function of the...
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Sunghan Kim (KTH Royal Institute of Technology)10/09/2026, 11:30Degenerate PDEs and Free Boundary Problems
Constraint maps are energy-minimizers under an image constraint, which is a natural vectorial extension of the obstacle problem. These maps develop free boundaries, due to the presence of an obstacle, while they also develop singularities, such as discontinuities, often for topological reasons. The partial regularity theory of these maps was established in the nineties, little has been known...
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65. Nonlocal-to-local convergence of convolution operators and its application to phase-field modelsPatrik Knopf (Karlsruher Institut für Technologie (KIT))10/09/2026, 11:30Phase Field Methods in Real-World Applications
The goal of nonlocal-to-local convergence is to show that certain singular, nonlocal convolution-type integral operators converge to a local differential operator as the convolution kernel concentrates at zero. This can be a useful tool in the physical justification of mathematical models (e.g., the Cahn-Hilliard equation), especially when a desired local differential operator cannot be...
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Sebastian Schwarzacher10/09/2026, 11:30Fluid-structure Interactions
In this lecture, I will summarize how variational methods can be used to establish the existence of weak solutions for fluid–structure interaction problems. In particular, I will discuss how PDEs with inertia can be approximated variationally using gradient-flow techniques. I will focus on results for largely deforming bulk solids interacting with fluids governed by the Navier–Stokes...
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Dr Hayk Mikayelyan (University of Nottingham Ningbo China)10/09/2026, 12:00Degenerate PDEs and Free Boundary Problems
Consider the cylindrical domain $\Omega=D\times(0,1)$ and the convex functional
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$$ \int_\Omega \frac{1}{2}|\nabla U(x)|^2dx +\int_D V(x')^+\,dx', $$ with nonlocal obstacle acting on function $V(x')=\int_0^1 U(x', t) dt $. We show that the unique minimizer solves the equation $$
\Delta U(x',x_n) = \chi_{{V>0}}(x') + \chi_{{V=0}}(x') [\partial_\nu U (x',0) + \partial_\nu U... -
Sebastian Aland (HTW Dresden & TU Freiberg)10/09/2026, 12:00Phase Field Methods in Real-World Applications
Growing tumors generate and respond to stress in their local environment. On the one hand, local cell divisions and death lead to complex strain patterns in the tissue. On the other hand, tissue re-arrangements can relax the resulting mechanical shear stresses and make the tissue more fluid-like. To predict the outcomes of these nonlinear visco-elastic interactions, we introduce the framework...
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Helmut Abels (Universität Regensburg)10/09/2026, 14:00Free Boundaries in Biology
We consider a system consisting of a surface Navier-Stokes equation for incompressible fluids on an elastic inextensible membrane, whose evolution is coupled to the flow of the fluid on the surface. This leads to a highly nonlinear quasilinear geometric evolution equation of parabolic-hyperbolic type. Using a suitable parametrization we linearize the system and obtain well-posedness of it in...
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Thomas Richter (Otto-von-Guericke Universität Magdeburg)10/09/2026, 14:00Fluid-structure Interactions
Living organisms such as fish propel themselves through periodic, self-generated deformations of their body shape. Modeling this motion within a fluid-structure interaction (FSI) framework requires a careful separation of the active deformation, which is prescribed and drives the motion, from the passive, resulting motion of the body, which follows the laws of rigid body dynamics. In this...
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Cintia Pacchiano (Universidad Nacional Autónoma de México)10/09/2026, 14:00Degenerate PDEs and Free Boundary Problems
In this talk, we present a unified regularity framework for variational integrals with non-uniformly elliptic integrands, including those exhibiting $p,q$-growth or exponential-type growth. We consider general energy functionals of the form
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$$ \int_{\Omega} f(x, Du) \, dx, $$ where the integrand $f(x, \xi)$ may satisfy natural growth, $(p,q)$-growth, or exponential growth conditions. We... -
Prof. Pierluigi Colli (University of Pavia)10/09/2026, 14:00Phase Field Methods in Real-World Applications
We consider a phase-field model for multiphase flows in porous media coupling a Brinkman equation for the fluid motion with a generalized Cahn–Hilliard equation accounting for curvature-driven effects and mass exchange. We discuss existence results for the coupled system and, under suitable assumptions, uniqueness and continuous dependence properties. We further investigate the asymptotic...
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Mingyue Zhang (TU Wien)10/09/2026, 14:30Free Boundaries in Biology
We study the asymptotic limits of a Keller--Segel system with porous-medium-type nonlinear diffusion and nonlinear logistic sensitivity. We identify three distinguished limits and clarify their connections with the original system. Depending on the parameter regimes, the model converges to a porous medium equation when the chemotactic sensitivity is weak and the chemical diffusion is slow, a...
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Edgard Pimentel (CMUC, University of Coimbra)10/09/2026, 14:30Degenerate PDEs and Free Boundary Problems
Fully nonlinear free transmission problems have been examined from a number of perspectives. These include the existence of solutions, regularity estimates and numerical methods. However, the uniqueness of solutions remains fairly open. We resort to a relaxed notion of viscosity solutions and relate it with the usual definition. We also impose conditions on the operators driving the free...
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Dominic Breit10/09/2026, 14:30Fluid-structure Interactions
We consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the Navier--Stokes equations. Consequently, damping within the coupled system comes entirely from the parabolic fluid subsystem. Our main result is the construction of a...
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Dr Disson dos Prazeres (Universidade Federal de Sergipe)10/09/2026, 15:00Degenerate PDEs and Free Boundary Problems
In this talk, we will discuss conditions for the existence of solutions exhibiting a dead core in nonlocal problems. In particular, we will analyze conditions that ensure the formation of a dead core, as well as existence arguments and examples illustrating this phenomenon in the context of nonlocal partial differential equations.
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Kei Fong Lam (Hong Kong Baptist University)10/09/2026, 15:00Phase Field Methods in Real-World Applications
Recent studies have shown that chemical reactions in phase separating systems can lead to growth and division of droplets. The fuel from chemical reactions can lead to a sequence of growth and splitting that mimics the behavior in the transition of protocells from nonliving to living systems. Such systems where energy is externally supplied and the governing equations do not fulfil a free...
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Matthieu Hillairet (Université de Montpellier)10/09/2026, 15:00Fluid-structure Interactions
Computing asymptotics of the Stokes problem in thin domains is a crucial issue in the analysis of fluid/solid problems. It enables a sharp description of the relative motion of particles that are close to contact and it is also a crucial step toward computing effective properties of mixtures in a dense regime. First results trace back to the book of Happel and Brenner (65’) using formal...
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Patrik Knopf (Karlsruher Institut für Technologie (KIT))10/09/2026, 15:00Free Boundaries in Biology
I will present a thermodynamically consistent model (from a collaboration with Y. Liu), which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which is determined by a Navier--Stokes equation. In order to take interactions between bulk and boundary into account, we...
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Giulia Cavalleri (WIAS)10/09/2026, 15:30Phase Field Methods in Real-World Applications
A diffuse interface model for tumour growth in the presence of a nutrient is introduced, incorporating mechanical effects and reversible tissue damage. The highly nonlinear PDE system consists of a Cahn–Hilliard equation governing the phase separation between healthy and tumour cells, coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance...
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Sebastian Hensel10/09/2026, 15:30Free Boundaries in Biology
The most basic examples of curvature driven interface evolution are gradient flows of the perimeter. I will discuss in this talk, at the example of Mullins-Sekerka flow, how the gradient-flow structure can be used to provide robust solution theories, bypassing the usage of comparison principles typically not available for such problems. I will focus on existence theory based on an energy...
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Dr Rafayel Teymurazyan (KAUST)10/09/2026, 15:30Degenerate PDEs and Free Boundary Problems
We present recent advances on the degenerate quenching problem. Our main result establishes the local finiteness of the (n-1)-dimensional Hausdorff measure of the free boundary. The proof combines optimal gradient decay estimates, derived from an intrinsic Harnack-type inequality, with a detailed analysis of the flatness regime, where minimizers enjoy improved regularity. This approach yields...
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Chandrasekhar Venkataraman (University of Sussex)10/09/2026, 16:30Plenary Talks
In the first part of the talk, we consider coupled bulk-surface reaction-diffusion systems modelling receptor-ligand dynamics on an evolving domain. In biologically relevant regimes, we derive various novel free-boundary problems as limits of the model. These limiting free-boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. Our results are new even in the...
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Klaus Deckelnick (Otto-von-Guericke-Universitaet Magdeburg)10/09/2026, 17:30Plenary Talks
Mean curvature flow evolves a family of hypersurfaces in such a way that the normal velocity is given by the mean curvature at each point of the surface. This fundamental geometric evolution law can be interpreted as the $L^2$-gradient flow of the area functional and has applications e.g. in materials science and image processing. The talk is concerned with the analysis of a numerical method...
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Pei SU11/09/2026, 09:00Fluid-structure Interactions
We study the interaction between a rigid body and an inviscid compressible fluid in a bounded domain. The fluid is described by the compressible Euler equations, while the rigid body obeys the laws of linear and angular momentum. We prove the existence and uniqueness of classical solutions to the resulting coupled fluid–structure interaction system. The analysis relies on a suitable...
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Aelson Sobral (King Abdullah University of Science and Technology)11/09/2026, 09:00Degenerate PDEs and Free Boundary Problems
We develop a unified variational framework for singular energies that arise as analytic models in Simon's symmetric minimal surface program. Motivated by the linearized profile $\Delta u \sim u^{-1}$, we study local minimizers of energies whose potential $\sigma$ may diverge at the origin. This class encompasses both the logarithmic potentials linked to the geometry of minimal cones and the...
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Kei Fong Lam (Hong Kong Baptist University)11/09/2026, 09:00Optimization and Free Boundaries
We study a phase-field structural topology optimization problem motivated by applications in 3D printing formulated using a thermoelastic Cosserat continuum framework with thermal spectral dissipation. The Cosserat theory accounts for micropolar effects in the mechanical response, while thermal effects account for heat-driven phenomena relevant to additive manufacturing. The resulting...
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Theresa Simon (University of Münster)11/09/2026, 09:00Free Boundaries in Biology
I will present an example for how to pass from a first order perimeter optimization problem to a second order curvature optimization problem. While the original model, a nonlocal isoperimetric problem, arises from mathematical physics, its limit is Euler’s elastica functional. This is the 2D analogue of the Willmore energy, which features prominently in the modeling of lipid bilayers....
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Philip Herbert (University of Sussex)11/09/2026, 09:30Optimization and Free Boundaries
In this talk, we consider the shape optimisation of a semi-linear elliptic equation. We use a $W^{1,\infty}$-steepest descent with Armio step size to perform the optimisation. In the infinite dimensional setting, we show the convergence of two-dimensional shapes under a mild assumption. We conclude with some numerical experiments.
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Jonas Haselböck (Universität Regensburg)11/09/2026, 09:30Free Boundaries in Biology
In recent years, interface models have become increasingly popular in mathematical biology for describing tumour growth. Among these, the Cahn–Hilliard–Biot model was the first to incorporate both mechanical stress and fluid flow through a heterogeneous, saturated porous medium. In subsequent works, the original model was further extended to include Kelvin–Voigt viscoelasticity. Since the...
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Prof. Arnab Roy (Basque Center for Applied Mathematics)11/09/2026, 10:00Fluid-structure Interactions
We consider the motion of a large number of heavy particles in
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a Newtonian fluid occupying a bounded spatial domain. When we say ``heavy", we mean a particle with a mass density that approaches infinity at an appropriate rate as its radius vanishes. We show that the collective effect of heavy particles on the fluid motion is similar to the Brinkman perturbation of the Navier-Stokes system... -
Marvin Weidner (University of Bonn)11/09/2026, 10:00Degenerate PDEs and Free Boundary Problems
A classical result by Kinderlehrer-Nirenberg states that C^{1,\alpha} regularity of the free boundary near a regular point implies that the free boundary is smooth. This principle applies to a wide range of free boundary problems for second-order operators. The goal of this talk is to explore counterparts of such higher regularity results for nonlocal free boundary problems, focusing on the...
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Katharina Hopf11/09/2026, 10:00Free Boundaries in Biology
Viscoelastic phase separation is thought to play an important role in cell biology. Differences in mechanical properties and relaxation times of the constituents can induce dynamic asymmetry during demixing, generating complex morphological transitions such as phase inversion, a characteristic feature of viscoelastic phase separation. In this talk, we determine the interface dynamics arising...
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Muhammad Uzair Qureshi11/09/2026, 10:00Optimization and Free Boundaries
Computational Fluid Dynamics (CFD) analysis of reactive flows over heterogeneous catalysts is a challenging task even for “simple” laminar flows. This involves solving a system of Partial Differential Equations (PDEs) with highly non-linear boundary conditions imposed by the surface chemistry which leads to stiffness and bad conditioning of the overall equation system requiring extensive...
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Igor Kukavica (University of Southern California)11/09/2026, 10:30Fluid-structure Interactions
We address a system of partial differential equations modeling the motion of an elastic body inside an incompressible fluid. The fluid is governed by the incompressible Navier-Stokes equations, while the structure is represented by the wave equation. In this talk, we review established local and global existence theorems and discuss recent developments in their long-time dynamics. These...
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Elisabetta Rocca (Università di Pavia)11/09/2026, 10:30Free Boundaries in Biology
In this talk we introduce a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the one of an additional variable $\sigma$ influencing the phase separation process. The main application of the model refers to cancer growth processes, where $\sigma$ may represent the concentration of a chemical substance affecting the...
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Balázs Kovács (Paderborn University)11/09/2026, 11:30Plenary Talks
In this talk we will present and discuss a fully discrete algorithm for mean curvature flow of closed surfaces using Lagrange multipliers for preserving the energy-decreasing structure. The algorithm is based on the solution-driven formulation using Huisken's evolution equations for the normal vector and the mean curvature. The method uses a high-order multistep methods in time and evolving...
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Maxim Olshanskii (University of Houston)11/09/2026, 12:30Plenary Talks
The talk concerns linear parabolic problems posed on time-dependent domains that may undergo topological changes. The domains are represented by smooth level-set functions and may split, merge, or develop or lose components and holes. Using the classification of generic transitions provided by Morse theory, we introduce anisotropic space-time function spaces adapted to the resulting singular...
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