Global well-posedness of a conservative relaxed cross diffusion system

Thomas Lepoutre; Michel Pierre; Guillaume Rolland

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arXiv · 1203.5989

Global well-posedness of a conservative relaxed cross diffusion system

Thomas Lepoutre·Michel Pierre·Guillaume Rolland

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Abstract

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_i\to \partial_tu_i-Δ(a_i(\tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent $I$ density-functions, $\tilde{u}$ is a spatially regularized form of $(u_1,...,u_I)$ 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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Thomas Lepoutre, Michel Pierre, Guillaume Rolland. 2012-03-27. Global well-posedness of a conservative relaxed cross diffusion system. https://arxiv.org/abs/1203.5989

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