Perturbative global solutions of a large class of cross diffusion systems in any dimension

2024/03/01 by Desvillettes, L, Moussa, A · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.00391

Abstract

This article focuses on a large family of cross-diffusion systems of the form ∂ t U-ΔA(U) = 0, in dimension d ∈ N * , and where U ∈ R 2. We show that under natural conditions on the nonlinearity A, those systems have a unique smooth (nonnegative for all components) solution when the initial data are small enough in a suitable norm.

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• Stability of non-conservative cross diffusion model and approximation by stochastic particle systems

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