Global Existence of Solutions to Reaction Diffusion Systems with Mass Transport Type Boundary Conditions

TL;DR

This paper proves the global existence of solutions for a class of reaction-diffusion systems involving boundary and interior reactions with mass transport, using classical potential theory and linear estimates.

Contribution

It introduces a framework for analyzing reaction-diffusion systems with boundary mass transport, establishing global solutions under new boundary conditions.

Findings

Established local well-posedness of the system.

Proved global existence of solutions.

Applied classical potential theory and linear estimates.

Abstract

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local well-posedness and global existence of solutions for these systems using classical potential theory and linear estimates for initial boundary value problems.