Critical Fujita exponent for a fast diffusive equation with variable coefficients

摘要

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