Maxime Breden, École Polytechnique
From Greg McCracken
Title: About the many equilibria of a cross-diffusion system in population dynamics
Abstract: Cross-diffusion is a mechanism that can be used in population dynamics to model a repulsive effect between individuals. Mathematically, this corresponds to adding nonlinear diffusion terms to classical reaction-diffusion systems. Cross-diffusion can generate a rich variety of solutions, whose qualitative behavior seems to better fit observations (including spatial segregation phenomenon), but it also complicates the mathematical study of these solutions. In this talk, I will explain how this problem can be tackled by combining numerical simulations with a posteriori estimates, to obtain computer-assisted proofs, and I will present some recent results about the steady states of the SKT system.