Uniform boundedness for reaction-diffusion systems with mass dissipation

TL;DR

This paper establishes conditions under which reaction-diffusion systems with mass dissipation have globally bounded classical solutions, using duality and heat operator regularization, with implications for the Global Attractor Conjecture.

Contribution

It provides new criteria for global existence and uniform bounds of solutions in reaction-diffusion systems with mass dissipation, especially when diffusion coefficients are close or large.

Findings

Global existence of solutions under certain diffusion conditions

Uniform-in-time bounds for classical solutions

Validation of the Global Attractor Conjecture in specific cases

Abstract

We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if the diffusion coefficients are close to each other, or if the diffusion coefficients are large enough compared to initial data, then the local classical solution exists globally and is bounded uniformly in time. Applications of the results include the validity of the Global Attractor Conjecture for complex balanced reaction systems with large diffusion.