Blow-up for a degenerate reaction–diffusion system with nonlinear localized sources

This paper deals with the global existence and blow-up of nonnegative solution of the degenerate reaction–diffusion system with nonlinear localized sources involved a product with local terms. We investigate the influence of localized sources and local terms on global existence and blow up for this system. Moreover, we establish the precise blow-up estimates. Finally, for the special case p1 = p2 = 0, we show the blow-up set is whole region and the uniform blow-up profiles are obtained. These extend a resent work of Chen and Xie in [Y. Chen, C. Xie, Blow-up for a porous medium equation with a localized source, Appl. Math. Comput. 159 (2004) 79–93], which considered the single equation with localized sources. © 2005 Elsevier Inc. All rights reserved