CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS

Title & Authors
CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS
Li, Zhongping; Mu, Chunlai; Du, Wanjuan;

Abstract
In this paper, we consider the positive solution to a Cauchy problem in $\small{\mathbb{B}^N}$ of the fast diffusive equation: $\small{{\mid}x{\mid}^mu_t={div}(\mid{\nabla}u{\mid}^{p-2}{\nabla}u)+{\mid}x{\mid}^nu^q}$, with nontrivial, nonnegative initial data. Here $\small{\frac{2N+m}{N+m+1}}$ < $\small{p}$ < 2, $\small{q}$ > 1 and 0 < $\small{m{\leq}n}$ < $\small{qm+N(q-1)}$. We prove that $\small{q_c=p-1{\frac{p+n}{N+m}}}$ is the critical Fujita exponent. That is, if 1 < $\small{q{\leq}q_c}$, then every positive solution blows up in finite time, but for $\small{q}$ > $\small{q_c}$, there exist both global and non-global solutions to the problem.
Keywords
critical Fujita exponent;fast diffusive equation;variable coefficients;
Language
English
Cited by
1.
Existence and nonexistence of global solutions for a semilinear reaction–diffusion system, Journal of Mathematical Analysis and Applications, 2017, 445, 1, 97
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