Multi-species Balance Laws

Head:
Katharina Hopf

Coworkers:
Moritz Immanuel Gau

Secretary:
Andrea Eismann

From left to right: Andrea Eismann, Katharina Hopf, 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
• Cauchy theory for hyperbolic-parabolic-elliptic systems
• Singularity formation and asymptotic analysis
• Entropy methods, stability estimates, and singular limits

Highlights