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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

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

Résumé

This article focuses on a large family of cross-diffusion systems of the form ∂ t U-∆A(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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Dates et versions

hal-04484591 , version 1 (29-02-2024)

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L Desvillettes, A Moussa. Perturbative global solutions of a large class of cross diffusion systems in any dimension. 2024. ⟨hal-04484591⟩
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