Oberseminar Angewandte Analysis
Das Oberseminar Angewandte Analysis ist eine gemeinsame Veranstaltung von Prof. P. Bella, Prof. M. Röger und Prof. B. Schweizer
| Datum | Sprecher | Herkunft | Titel/Bemerkung |
| 07.01.2026 | Markus Gahn | Augsburg | Effective interface laws of Navier-slip-type for Stokes flow through thin elastic porous layers ____________________________________ We rigorously derive effective interface laws governing fluid flow through a thin elastic porous membrane separating two bulk fluid domains. The microscopic geometry consists of a periodically structured membrane composed of an elastic solid and fluid-filled pores, with characteristic thickness and periodicity of order ε, small compared to the size of the bulk regions. The underlying model couples instationary Stokes flow with linear elasticity for the solid, with different scalings of the elastic stress tensor, leading to qualitatively different macroscopic behavior. The derivation of the macroscopic model is based on compactness methods with respect to the two-scale convergence adapted to thin domains with oscillatory microstructure, where the membrane is asymptotically reduced to an effective interface. Across this interface, transmission conditions of Navier-slip type are derived, incorporating dynamic displacement effects. Depending on the scaling for the elasticity tensor, the effective displacement satisfies either a membrane-type equation or a Kirchhoff-Love plate equation. The resulting interface laws naturally allow for mass exchange between the adjacent fluid regions. |
| 19.11.2025 | Leonard Kreutz | München | Γ-EXPANSION OF THE CAHN-HILLIARD FUNCTIONAL WITH DIRICHLET BOUNDARY CONDITIONS ___________________________________________ Abstract: In this talk, we present the second-order asymptotic development of the Cahn-Hilliard functional under Dirichlet boundary conditions via Γ-convergence. We begin by reviewing results from the literature on the asymptotic expansion of the Cahn-Hilliard functional. Subsequently, we discuss our ongoing research focused on the Cahn-Hilliard functional with Dirichlet boundary conditions. In particular, we examine the case where no interior interfaces are present and highlight several open questions for future investigation. This seminar is based on work in collaboration with Irene Fonseca and Giovanni Leoni. |
| 12.11.2025 | Carlo Sportolari | Düsseldorf | |
| 22.10.2025 | Lukas Niebel | Münster | Critical trajectories in kinetic geometry ----------------------------------------------------- Kinetic equations such as the Kolmogorov equation arise naturally in statistical physics, but they exhibit a hypoelliptic structure that makes classical regularity tools like the De~Giorgi-Nash-Moser theory difficult to adapt. A central challenge is to understand the geometry underlying the transport–diffusion interaction. |
| 09.07.2025 | Vlad Stefan Revnic | Heidelberg | Rigorous Derivation of Darcy´s Law for Thin Perforated Layers with Different Thickness |
| 23.06.2025 | Benjamin Lledos | Nîmes | Continuity of the stress field for a solution of a minimization problem with linear growth |
| 14.05.2025 | Akram Sharif | Dresden | Mathematical foundations of contact interactions in continuum mechanics |
| 22.01.2025 | Balázs Kovács | Paderborn | Numerical surgery for mean curvature flow of surfaces --- A numerical analyst at the operating table |
| 06.11.2024 | Gregoire Allaire | Paris | Optimal design of lattice or architectured materials by an homogenization approach |
| 29.07.2024 | Lukas Fix | Heidelberg | Elliptic Regularity Theory for the Robin Laplacian in Domains with an Exterior Cusp |
| 16.07.2024 | Chiara Gavioli | Italien | Hysteresis in porous media |
| 17.04.2024 | Benoît Van Vaerenbergh | Louvain-la-Neuve | Asymptotic behavior of p-Harmonic mappings when p goes to |
| 06.03.2024 | Heiner Olbermann | Louvain-la-Neuve | Sharp Ridges in a Variational Problem for Convex Functions |
| 05.12.2023 um 14:15 Uhr im E29 | Sören Bartels | Freiburg | Modeling and simulation of thin sheet folding |