Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects

TL;DR

This paper establishes the global existence of solutions for reaction-diffusion systems with minimal assumptions, focusing on cross-absorptive effects, nonlinear diffusion, and avoiding entropy estimates.

Contribution

It introduces a generalized solution concept and proves global existence under relaxed conditions, expanding applicability to systems with cross-absorptive interactions.

Findings

Global solutions exist under minimal assumptions

Applicable to nonlinear diffusion systems

Does not rely on entropy estimates

Abstract

We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.