Blow-up in reaction-diffusion systems under Robin boundary conditions

TL;DR

This paper demonstrates that reaction-diffusion systems with Robin boundary conditions can exhibit finite-time blow-up solutions, providing bounds on the blow-up time through differential inequality techniques.

Contribution

It applies the differential inequality method to reaction-diffusion systems with Robin boundary conditions, establishing conditions for blow-up and bounds on blow-up time.

Findings

Reaction-diffusion systems can blow up under Robin boundary conditions.

Upper bounds for blow-up time are derived.

Lower bounds for blow-up time are provided for specific nonlinearities.

Abstract

In this paper we apply the differential inequality technique of Payne {\it et. al} \cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a particular nonlinearity, a lower bound on the blow-up time, when blow-up does occur, is also given.