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http://dx.doi.org/10.4134/BKMS.2013.50.1.105

CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS  

Li, Zhongping (College of Mathematic and Information China West Normal University)
Mu, Chunlai (College of mathematics and Statistics Chongqing University)
Du, Wanjuan (College of Mathematic and Information China West Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 105-116 More about this Journal
Abstract
In this paper, we consider the positive solution to a Cauchy problem in $\mathbb{B}^N$ of the fast diffusive equation: ${\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}$ < $p$ < 2, $q$ > 1 and 0 < $m{\leq}n$ < $qm+N(q-1)$. We prove that $q_c=p-1{\frac{p+n}{N+m}}$ is the critical Fujita exponent. That is, if 1 < $q{\leq}q_c$, 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.
Keywords
critical Fujita exponent; fast diffusive equation; variable coefficients;
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