Cross-diffusion in Population dynamics: triangular structure; Dr. Ariane Trescases (Institut de Mathematiques de Toulouse)

ABSTRACT: In Population dynamics, reaction-cross diffusion systems model the evolution of populations of multiple species with a repulsive effect between individuals. For these strongly coupled nonlinear systems, a question as basic as the existence of solutions appears to be extremely complex. In this talk, we consider two-species cases where cross diffusion terms appear only in one of the two equations (triangular case). We will address questions of existence of solutions, an approximation through a microscopic model, and an application to chemotaxis.