slideshow 3

Seminar on partial differential equations

Analysis of diffusive population systems for multiple species

Ansgar Jüngel
TU Wien

 

Tuesday, 23. October 2018 - 9:00 to 10:00

in IM, rear building, ground floor

The dynamics of multi-species populations can be described by random walks on a lattice which leads in the diffusive limit to nonlinear reaction-cross-diffusion systems. A special model was suggested by Shigesada, Kawasaki, and Teramoto in 1979. The diffusion matrix of these cross-diffusion systems is typically neither symmetric nor positive definite, which complicates the analysis. The idea is to reveal a so-called entropy structure (which is a special Lyapunov functional) allowing for gradient estimates. In this talk, we review recent results on population cross-diffusion models, including the local and global existence analysis, uniqueness of weak solutions, and their large-time asymptotics.