Free Boundary Problems 2026

Session

Optimization and Free Boundaries

MS-4

10 Sept 2026, 10:30

Humboldt Universität zu Berlin

Conveners

Optimization and Free Boundaries: MS-4-1

• Amal Alphonse
• Michael Hintermüller (Weierstrass Institute Berlin)
• Michael Hinze (Universität Koblenz)

Optimization and Free Boundaries: MS-4-2

• Michael Hinze (Universität Koblenz)
• Amal Alphonse
• Michael Hintermüller (Weierstrass Institute Berlin)

Description

Organisers: Amal Alphonse, Michael Hintermüller, Michael Hinze

125. Gradient Flow Dynamical System for Free Boundary Problems

Prof. Jan Sokolowski (Systems Research Institute of the Polish Academy of Sciences)

10/09/2026, 10:30

Optimization and Free Boundaries

We present new analytical results on the gradient flow dynamical system (GFDS) method for free boundary problems. The representative model is the interior two-dimensional Bernoulli problem. Let $\Omega\subset\mathbb{R}^{2}$ be a fixed smooth domain. The unknowns are a smooth Jordan curve $\Gamma=f(\mathbb{S}^{1})\Subset\Omega$ and a harmonic potential $u$ in the annular region...

131. Proximal Point Methods for Variational Inequalities and Free Boundaries

Chenghao Dong (University of Oxford)

10/09/2026, 11:00

Optimization and Free Boundaries

Variational inequalities provide a natural mathematical language for obstacle, contact, and free-boundary phenomena. A typical problem considered in this talk is the constrained minimisation problem
$$\min_{u\in K} J(u), \qquad K=\{u\in U:\mathcal Bu(x)\in C(x)\ \text{a.e. on }\Omega_d\},$$ where $u$ is the state variable, $U$ is its function space, $J:U\to\mathbb R$ is the energy, $\mathcal...

148. Can we Control the Free Boundary in the Obstacle Problem?

José Francisco Rodrigues (Universidade de Lisboa)

10/09/2026, 11:30

Optimization 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...

112. Optimal design of linearly Cosserat and thermal spectral structures: A phase field approach

Kei Fong Lam (Hong Kong Baptist University)

11/09/2026, 09:00

Optimization 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...

114. Convergence of a shape optimisation algorithm for a semi-linear elliptic equtions in function spaces using $W^{1,\infty}$-steepest descent

Philip Herbert (University of Sussex)

11/09/2026, 09:30

Optimization 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.

23. Reduced Order CFD based Reactor Shape Optimization for Heterogeneous Catalytic Systems

Muhammad Uzair Qureshi

11/09/2026, 10:00

Optimization 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...