On Blow-up Solutions of A Parabolic System Coupled in Both Equations and Boundary Conditions

Abstract

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

Keywords

• Rection-Diffusion equation; Blow-up set; Blow-up rate estimate; Comparison principle; Radial function