OverviewThe 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".
- 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
- Consistent numerical approximations and their convergence
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.