Existence of solutions of a non linear cross diffusion system arising in population dynamics
We present results on existence of solutions for a strongly coupled cross-diffusion model for two competing species based on a semidiscretization in time. The variables are the population densities of the species. Existence of strictly positive weak solutions to the semidiscrete problem is proved. Moreover, it is shown that the semidiscrete solutions converge to a solution of the continuous problem. The proofs are based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional.
Gonzalo Galiano, Universidad de Oviedo, Spain
December 15, 2000