一类带梯度项的快速反应扩散方程解的熄灭

Extinction for the Fast Diffusion Equations with Nonlinear Gradient Absorption

讨论了一类快速反应扩散方程u_1=△u^(?)+λ|▽u|^(?)在全空间上Cauchy问题.当p>2,0<m<(N-2)/N时,若初值满足适当的衰减条件,则方程的解会熄灭.反之,则不会熄灭.

This paper is to deal with the Cauchy problem of the fast diffusion equation us=-△u^m＋λ｜△↓u｜^p in R^N.It is shown that if p〉2,0〈m〈N-2/N , the solution vanishes in finite time with the initial data satisfying some decay conditions at ｜x｜= ∞ and that the solution is strictly positive in RN if the initial data does not satisfy such decay conditions.