Global Existence of Solutions to Reaction Diffusion Systems with Mass Transport Type Boundary Conditions on an Evolving Domain

TL;DR

This paper proves the global existence of non-negative solutions for reaction-diffusion systems with mass transport boundary conditions on evolving domains, using Lyapunov functionals and duality methods.

Contribution

It introduces a novel approach to establish global solutions for reaction-diffusion systems with complex boundary conditions on dynamic domains.

Findings

Proved global existence of solutions under specified conditions

Applied Lyapunov functional and duality techniques

Addressed reaction-diffusion systems on evolving domains

Abstract

We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish the existence of component-wise non-negative global solutions.