CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS

被引：2
|
作者：
Li, Zhongping [1 ]
Mu, Chunlai [2 ]
Du, Wanjuan [1 ]
机构：
[1] China West Normal Univ, Coll Math & Informat, Nanchong 637009, Peoples R China
[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2013年 / 50卷 / 01期
关键词：
critical Fujita exponent; fast diffusive equation; variable coefficients; DEGENERATE PARABOLIC EQUATION; LARGE TIME BEHAVIOR; BLOW-UP; FILTRATION EQUATION; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; NONEXISTENCE; EXISTENCE;
D O I：
10.4134/BKMS.2013.50.1.105
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the positive solution to a Cauchy problem in R-N of the fast diffusive equation: vertical bar x vertical bar(m)u(t) = div(vertical bar del(u)vertical bar(p-2)del(u)) + vertical bar x vertical bar(n)(q)(u), with nontrivial, nonnegative initial data. Here 2N+m/N+m+1 < p < 2, q > 1 and 0 < m <= n < qm+N(q-1). We prove that q(c) = p-1+p+n/N+m is the critical Fujita exponent. That is, if 1 < q <= q(c), then every positive solution blows up in finite time, but for q > q(c), there exist both global and non-global solutions to the problem.
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页码：105 / 116
页数：12
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