Life span and a new critical exponent for a quasilinear degenerate parabolic equation with slow decay initial values

被引:19
作者
Mu, Chunlai [1 ]
Li, Yuhuan [2 ]
Wang, Ying [3 ]
机构
[1] Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China
[2] Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China
[3] Univ Elect Sci & Technol China, Sch Appl Math, Chengdu 610054, Peoples R China
基金
中国国家自然科学基金;
关键词
Blow-up; Life span; Global existence; Critical exponent; Degenerate parabolic equation; Slowly decay initial data; SEMILINEAR HEAT-EQUATION; LARGE TIME BEHAVIOR; CAUCHY-PROBLEM; BLOW-UP; DIFFUSION EQUATION; GLOBAL EXISTENCE; NONEXISTENCE; THEOREMS; SYSTEMS; TRACES;
D O I
10.1016/j.nonrwa.2008.10.048
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the positive solution of a Cauchy problem for the following P-Laplace parabolic equation u(t) = div(|del u|(p-2)del u) + u(q), p > 2, q > 1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence of global and nonglobal solutions of the Cauchy problem. Furthermore, the life span of solutions is also studied. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:198 / 206
页数:9
相关论文
共 36 条
[1]  
ALIKAKOS ND, 1983, J MATH PURE APPL, V62, P253
[2]  
[Anonymous], J DIFF EQNS
[3]  
[Anonymous], ARCH RATIONAL MECH A
[4]   The role of critical exponents in blow-up theorems: The sequel [J].
Deng, K ;
Levine, HA .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 243 (01) :85-126
[5]   ON THE CAUCHY-PROBLEM AND INITIAL TRACES FOR A DEGENERATE PARABOLIC EQUATION [J].
DIBENEDETTO, E ;
HERRERO, MA .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 314 (01) :187-224
[6]  
DIBENEDETTO E, 1985, J REINE ANGEW MATH, V357, P1
[7]  
Fujita H., 1966, J. Fac. Sci. Univ. Tokyo Sec. 1A Math, V16, P105
[8]  
Galaktionov V. A., 1980, Soviet Physics - Doklady, V25, P458
[9]  
Galaktionov V. A., 1995, DEGRUYTER EXPOSITION
[10]   A general approach to critical Fujita exponents in nonlinear parabolic problems [J].
Galaktionov, VA ;
Levine, HA .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 34 (07) :1005-1027