Head:
Katharina Hopf
Coworkers:
Moritz Immanuel Gau
Team Assistant:
Andrea Eismann
Research topics:
Katharina Hopf
Coworkers:
Moritz Immanuel Gau
Team Assistant:
Andrea Eismann
Andrea Eismann, Moritz Immanuel Gau.
Overview
The group is devoted to the mathematical analysis of strongly coupled PDE systems modelling the evolution of interacting species with different mechanical properties. Such systems are prone to instabilities, leading to significant challenges in their mathematical analysis and numerical approximation. The group focusses on thermodynamically compatible models with an underlying entropy structure. An overarching goal is to develop entropy/energy-based methods for understanding regimes of (in-)stability. At present, our main applications are cross-diffusion systems and reactive mixtures, as well as two-phase flow and viscoelastic materials. Within WIAS the group has co-operations with the Research Groups "Partial Differential Equations", "Numerical Mathematics and Scientific Computing", and "Thermodynamic Modeling and Analysis of Phase Transitions".Research topics:
- Analysis of nonlinear partial differential equations
- Cross-diffusion, reaction-diffusion; interface phenomena
- Low regularity solutions and singularities
- Entropy tools and variational methods
Highlights
The MATH+ project proposal "Emergent structures in multi-component systems for embryogenesis" by the principal investigators Katharina Hopf, Matthias Liero (both WIAS), and Markus Mittnenzweig (Max Delbrück Center) has been approved in June 2025.
The article ”Convergence of a finite volume scheme and dissipative measure-valued--strong stability for a hyperbolic-parabolic cross-diffusion system” by Katharina Hopf and Ansgar Jüngel has been accepted and published open access by the journal ”Numerische Mathematik” in May 2025.
GAMM 2025, 95th Annual GAMM Meeting, Poznan, 07--11 April 2025,
Section 14 “Applied Analysis" organised jointly by Tomasz Dębiec (U Warsaw), Sebastian Hensel (U Bonn), and Katharina Hopf (WIAS).
Section 14 “Applied Analysis" organised jointly by Tomasz Dębiec (U Warsaw), Sebastian Hensel (U Bonn), and Katharina Hopf (WIAS).
Workshop "Energetic Methods for Multi-Component Reactive Mixtures - Modelling, Stability, and Asymptotic Analysis" hosted by WIAS, 13-15 September 2023. It was organised jointly with Michael Kniely (RG 1) and Ansgar Jüngel (TU Wien). Support by the DFG is gratefully acknowledged.
Flexible Research Platform
