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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 109546, 19 pages
http://dx.doi.org/10.1155/2012/109546
Research Article

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 8 January 2012; Accepted 26 April 2012

Academic Editor: Yong Hong Wu

Copyright © 2012 Pan Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|um|p2ul)+uq,  (x,t)RN×(0,T), where N1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.