Blow-up Properties of a Coupled System of Reaction-Diffusion Equations

Abstract

    This paper is concerned with a Coupled Reaction-diffusion system defined in a ball with homogeneous Dirichlet boundary conditions. Firstly, we studied the blow-up set showing that, under some conditions, the blow-up in this problem occurs only at a single point. Secondly, under some restricted assumptions on the reaction terms, we established the upper (lower) blow-up rate estimates. Finally, we considered the Ignition system in general dimensional space as an application to our results.