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

Sorbonne Université
Université Paris Cité

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	103686
Journal	Bulletin des Sciences Mathematiques
Volume	204
DOIs	https://doi.org/10.1016/j.bulsci.2025.103686
Publication status	Published - 1 Sept 2025

Keywords

Cross-diffusion
PDE
Parabolic
Population dynamics

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10.1016/j.bulsci.2025.103686

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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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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

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JO - Bulletin des Sciences Mathematiques

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

Abstract

Keywords

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