Global smooth solutions for triangular reaction-cross diffusion systems

2022/02/21 by Jessica Guerand, Guerand, Jessica, Angeliki Menegaki +3 · 1 citation
Mathematics · Medicine · Social Sciences · #Analysis of PDEs (math.AP) #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2202.10256

openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This class of systems arises in Population dynamics, and extends the triangular Shigesada-Kawasaki-Teramoto system when general power-laws growth are considered in the reaction and diffusion rates.

Citations

• Quantitative regularity for parabolic De Giorgi classes

Cited by

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

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