An existence result for a degenerate cross-diffusion system

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Havva Yoldas (T.U. Delft)

Resumen: We look at a cross-diffusion system consisting of two Fokker-Planck equations where the gradient of the density for each species acts as a potential for the other one. It is a degenerate system in the sense that it loses its parabolic behavior on some part of the domain. However, the system is also the gradient flow for the Wasserstein distance of a functional which is not lower semicontinuous. We then compute the convexification of the integrand (thus the lower semi continuous envelope of the functional) and provide an existence result in a suitable sense for the gradient flow of the corresponding relaxed functional. This is a joint work with R. Ducasse (Paris) and F. Santambrogio (Lyon).