Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(1): 105-116

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.105

Copyright © The Korean Mathematical Society.

Critical Fujita exponent for a fast diffusive equation with variable coefficients

Zhongping Li, Chunlai Mu, and Wanjuan Du

China West Normal University, Chongqing University, China West Normal University

Abstract

In this paper, we consider the positive solution to a Cauchy problem in $\mathbb R^N$ of the fast diffusive equation: $|x|^mu_t={\rm div}(|\nabla u|^{p-2}\nabla u)+|x|^nu^q$, with nontrivial, nonnegative initial data. Here $\frac{2N+m}{N+m+1}1$ and $0q_c$, there exist both global and non-global solutions to the problem.

Keywords: critical Fujita exponent, fast diffusive equation, variable coefficients

MSC numbers: 35K50, 35K55, 35B33