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Talk

Partial Hölder Regularity for a Class of Cross-Diffusion Systems with Entropy Structure

  • Claudia Raithel (Universität Wien)
E1 05 (Leibniz-Saal)

Abstract

We obtain partial $C^{0,\alpha}$-regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear parabolic systems. Under slightly more restrictive assumptions, we obtain partial $C^{1,\alpha}$-regularity. The cross-diffusion systems that we consider have a formal gradient flow structure, in the sense that they are formally identical to the gradient flow of a convex entropy functional. The main novel tool that we use is a "glued entropy density", which allows us to emulate the classical theory of partial Hölder regularity for nonlinear parabolic systems. We are, in particular, able to obtain partial $C^{1,\alpha}$-regularity for solutions of the Maxwell-Stefan system, as well as partial $C^{1,\alpha}$-regularity for bounded solutions of the Shigesada-Kawasaki-Teramoto model.

This talk is based on joint work with Marcel Braukhoff and Nicola Zamponi.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher