Global well-posedness of a conservative relaxed cross diffusion system

2012/03/27 by Lepoutre, Thomas, Pierre, Michel, Rolland, Guillaume
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.5989

Abstract

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form u_i→ ∂_tu_i-Δ(a_i(u)u_i) where the u_i, i=1,...,I represent I density-functions, u is a spatially regularized form of (u₁,...,u_I) and the nonlinearities a_i are merely assumed to be continuous and bounded from below. Existence of global weak solutions is obtained in any space dimension. Solutions are proved to be regular and unique when the a_i are locally Lipschitz continuous.

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