Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions

2015/11/13 by Klemens Fellner, Fellner, Klemens, Evangelos Latos +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35A01 #35B40 #35K57 #35K61 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1511.04349

openalex publication_date 2015/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time L¹ a-priori estimates, for instance, as a consequence of suitable mass conservation laws. A new result on the global existence of classical solutions is proved in three and higher space dimensions by combining regularity and interpolation arguments in Bochner spaces, a bootstrap scheme and a weak comparison argument. Moreover, provided that the considered system allows for entropy entropy-dissipation estimates proving exponential convergence to equilibrium, we are also able to prove that solutions are bounded uniformly-in-time.

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