Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions

TL;DR

This paper investigates the conditions under which reaction-diffusion equations with nonlinear dynamical boundary conditions are well-posed, globally exist, or blow up, providing new insights into their mathematical behavior.

Contribution

It introduces new results on local well-posedness, global existence, and blow-up phenomena for these complex boundary-coupled reaction-diffusion systems.

Findings

Established criteria for local well-posedness.

Identified conditions leading to blow-up.

Demonstrated scenarios for global existence.

Abstract

The paper deals with local well-posedness, global existence and blow-up results for reaction--diffusion equations coupled with nonlinear dynamical boundary conditions.