Orateur
Laurent Desvillettes
Description
We present a work in collaboration with Hector Bouton and Helge Dietert, in which we prove that the solutions to the triangular SKT (Shigesada-Kawasaki-Teramoto) cross diffusion system (a system appearing in the dynamics of populations in competition) are strong in dimension 3 (it was proven in dimension 2 by Lou, Ni and Wu in the 90s). The proof uses a new approach to the Krylov-Safonov theory, in the special case when the solution is increasing with time.