Blow-up rate estimates for a doubly coupled reaction–diffusion system

This paper deals with a reaction–diffusion system with coupled nonlinear inner sources and a nonlinear boundary flux. Blow-up rates are determined for four different blow-up situations. The socalled characteristic algebraic system is introduced to get a very simple and clear description for the desired blow-up rate estimates. It is pointed out that one cannot directly use super and sub-solutions to establish blow-up rate estimates, since they do not share the same blow-up time in general.  2005 Elsevier Inc. All rights reserved.