Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

2025/03/11 by Hector Bouton, Bouton, Hector, Laurent Desvillettes +3
Engineering · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.08186

openalex publication_date 2025/03/11 · openalex created_date 2025/10/07 · openalex updated_date 2026/07/28

Abstract

We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions. A key part is the independent careful study of the parabolic equation a∂_t w - Δw = f with a rough coefficient a, homogeneous Neumann boundary conditions, and the special assumption ∂_tw ≥ 0. By the same method, we obtain estimates for solutions to reaction-diffusion systems modelling reversible chemistry.

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