Free Boundary Problems 2026

Session

Phase Transitions and Pattern Formation

MS-8

8 Sept 2026, 14:00

Humboldt Universität zu Berlin

Conveners

Phase Transitions and Pattern Formation: MS-8-1

• Patrik Knopf (Karlsruher Institut für Technologie (KIT))
• Helmut Abels (Universität Regensburg)

Phase Transitions and Pattern Formation: MS-8-2

• Patrik Knopf (Karlsruher Institut für Technologie (KIT))
• Helmut Abels (Universität Regensburg)

Phase Transitions and Pattern Formation: MS-8-3

• Helmut Abels (Universität Regensburg)
• Patrik Knopf (Karlsruher Institut für Technologie (KIT))

Description

Organisers: Helmut Abels, Patrik Knopf

102. Analysis of an Allen--Cahn system in two scale topology optimization

Robert Lasarzik (WIAS)

08/09/2026, 14:00

Phase 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...

53. Stochastic phase-separation driven by transport noise

Luca Scarpa (Politecnico di Milano)

08/09/2026, 14:30

Phase 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
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...

74. On the numerical treatment of the stochastic Cahn-Hilliard equation with singular potential

Stefan Metzger (Friedrich-Alexander-Universität Erlangen-Nürnberg)

08/09/2026, 15:00

Phase 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...

45. Anisotropic crystal growth on surfaces

Robert Nürnberg

08/09/2026, 15:30

Phase Transitions and Pattern Formation

We consider a phase field model for crystal growth on a curved surface.
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...

17. Phase-field models for growing viscoelastic solids

Ulisse Stefanelli (Unviersity of Vienna)

09/09/2026, 10:30

Phase 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...

80. Discretization of Cahn--Hilliard equations with dynamic boundary conditions: error estimates and adaptivity

Nils Bullerjahn

09/09/2026, 11:00

Phase 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...

98. Gradient flows of degenerate viscoelastic phase separation

Moritz Gau (WIAS Berlin)

09/09/2026, 11:30

Phase 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...

88. Local Well-posedness of a Diffuse Interface Two-phase Flow Model with Surfactants

Songzhuang Chen

09/09/2026, 12:00

Phase 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...

76. Incompressible limit and pressure jump in the Cahn-Hilliard equation

Charles Elbar (Université Claude Bernard Lyon 1)

09/09/2026, 14:00

Phase 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.

72. Global Weak Solutions to the Cahn–Hilliard Equation with Degenerate Mobility and Singular Diffusion

Andrea Giorgini (Politecnico di Milano)

09/09/2026, 14:30

Phase Transitions and Pattern Formation

In this talk, I will present recent results on the existence of global weak solutions to the Cahn–Hilliard equation with degenerate mobility and singular diffusion. This model describes phase separation dynamics in polymer blends and is driven by the Flory–Huggins–de Gennes free energy.

14. A new approach to convergence to equilibrium for Cahn--Hilliard type equations with non-degenerate mobility

Andrea Poiatti (University of Parma)

09/09/2026, 15:00

Phase 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...

63. Sharp Interface Limit of a 3D Navier--Stokes/Allen--Cahn system

Yadong Liu (Nanjing Normal University)

09/09/2026, 15:30

Phase 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...