Blow-up properties for a degenerate parabolic system with nonlinear localized sources

摘要

In this paper, we investigate the initial-boundary problem of a degenerate parabolic system with nonlinear localized sources. We classify the blow-up solutions into global blow-up cases and single-point blow-up cases according to the values of m,n,pi,qi. Furthermore, we obtain the uniform blow-up profiles of solutions for the global blow-up case. Finally, we give some numerical examples to verify the results. These extend and generalize a recent work of one of the authors [L. Du, Blow-up for a degenerate reaction–diffusion systems with nonlinear localized sources, J. Math. Anal. Appl. 324 (2006) 304–320], which only considered uniform blow-up profiles under the special case p1=p2=0.