论文成果
The critical Fujita exponent for the fast diffusion equation with potential
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- 论文类型：期刊论文
- 发表时间：2013-02-15
- 发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- 收录刊物：SCIE、Scopus
- 文献类型：J
- 卷号：398
- 期号：2
- 页面范围：879-885
- ISSN号：0022-247X
- 关键字：Critical Fujita exponent; Fast diffusion; Potential; Global solutions;
Blow-up
- 摘要：This paper studies the Cauchy problem for positive solutions of the fast diffusion equation with source and quadratically decaying potential u(t) = Delta u(m) - V(x)u(m) + u(P) in R-n x (0, T), where 1 - 2/m alpha+n < m < 1, p > 1, n >= 2, V(x) similar to omega/vertical bar x vertical bar(2) with omega >= 0 as vertical bar x vertical bar -> infinity, and alpha is the positive root of m alpha (m alpha + n - 2) - w = 0. We obtain the critical Fujita exponent Pc = m to the problem in the sense that every nontrivial solution blows up in finite time when 1 < p <= pc, and there are both global and non-global solutions if p > pc. (C) 2012 Elsevier Inc. All rights reserved.
