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

L. Desvillettes; A. Moussa

doi:10.1016/j.bulsci.2025.103686

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

L. Desvillettes
, A. Moussa

École Polytechnique

Université Paris Cité

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

This article focuses on a large family of cross-diffusion systems of the form ∂_tU−ΔA(U)=0, in dimension d∈N^⁎, and where U∈R². 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.

langue originale	Anglais
Numéro d'article	103686
journal	Bulletin des Sciences Mathematiques
Volume	204
Les DOIs	https://doi.org/10.1016/j.bulsci.2025.103686
état	Publié - 1 sept. 2025

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10.1016/j.bulsci.2025.103686

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title = "Perturbative global solutions of a large class of cross diffusion systems in any dimension",

abstract = "This article focuses on a large family of cross-diffusion systems of the form ∂tU−ΔA(U)=0, in dimension d∈N⁎, and where U∈R2. 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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author = "L. Desvillettes and A. Moussa",

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AU - Moussa, A.

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N2 - This article focuses on a large family of cross-diffusion systems of the form ∂tU−ΔA(U)=0, in dimension d∈N⁎, and where U∈R2. 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.

AB - This article focuses on a large family of cross-diffusion systems of the form ∂tU−ΔA(U)=0, in dimension d∈N⁎, and where U∈R2. 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.

KW - Cross-diffusion

KW - PDE

KW - Parabolic

KW - Population dynamics

UR - https://www.scopus.com/pages/publications/105008771871

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DO - 10.1016/j.bulsci.2025.103686

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

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