Secondary critical exponent, large time behavior and life span for a quasilinear parabolic equation with slowly decaying initial values

被引：0
作者：
Yongsheng Mi
Chunlai Mu
Rong Zeng
机构：
[1] Chongqing University,College of Mathematics and Statistics
[2] Yangtze Normal University,College of Mathematics and Computer Sciences
来源：
Zeitschrift für angewandte Mathematik und Physik | 2011年 / 62卷
关键词：
Blow-up; Global existence; Critical exponent; Large time behavior; Life span; 35B33; 35k15; 35K65;
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学科分类号：
摘要：
In this paper, we consider the positive solution of the Cauchy problem for the following doubly degenerate parabolic equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_t-{\rm div}(|\nabla u|^{p} \nabla u^m)=u^q$$\end{document}with p > 0, q > 1,m > 1, and initial value decaying at infinity and give a new secondary critical exponent for the existence of global and nonglobal solutions. Furthermore, the large time behavior and the life spans of solutions are also studied.
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页码：961 / 978
页数：17
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