Global existence for semilinear reaction-diffusion systems on evolving domains

TL;DR

This paper proves global existence of solutions for reaction-diffusion systems on evolving domains, extending fixed domain results to dynamic settings without sign restrictions on growth, and supports findings with numerical simulations.

Contribution

It introduces a novel extension of reaction-diffusion global existence results to isotropically evolving domains without growth sign assumptions.

Findings

Global existence established for reaction-diffusion systems on evolving domains.

Results applicable to many pattern formation systems.

Numerical simulations confirm theoretical predictions.

Abstract

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.