Global Existence for Reaction-Diffusion Systems on Multiple Domains

Abstract

In this work, we study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a different domain that intersects with the first. The question addressed is related to the long standing question of global existence for reaction-diffusion systems with quasi-positive reaction vector fields that dissipate mass, in the setting of a single bounded spatial domain. The results extend recent work of the authors and others for systems on a single domain with L∞ diffusion and quasi-positive reaction vector fields that dissipate mass, in the setting of multiple domains.