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

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.

Key words: reaction-diffusion equations, mass transport, conservation of mass, Laplace Beltrami operator, global existence, a priori estimates