Global existence for reaction-diffusion systems with dissipation of mass and quadratic growth

TL;DR

This paper proves global classical solutions for reaction-diffusion systems with quadratic growth, mass and entropy dissipation, extending previous results to higher dimensions and simplifying the proof.

Contribution

It establishes global existence for reaction-diffusion systems with quadratic nonlinearities under dissipation conditions, without requiring mass conservation in higher dimensions.

Findings

Global classical solutions exist in any space dimension.

The proof is simpler than previous methods.

Results extend to systems with mass and entropy dissipation.

Abstract

We consider the Neumann and Cauchy problems for positivity preserving reaction-diffusion systems of $m$ equations enjoying the mass and entropy dissipation properties. We show global classical existence in any space dimension, under the assumption that the nonlinearities have at most quadratic growth. This extends previously known results which, in dimensions $n\ge 3$, required mass conservation and were restricted to the Cauchy problem. Our proof is also simpler.