一类带非线性项的拟线性抛物方程解的熄灭问题

Extinction for a Quasi-linear Parabolic Equation with Non-linear Source

研究了形如ut-div[σ(|▽u|2)▽u]=h(x)up的拟线性抛物方程在RN中有界凸空间上解的熄灭问题,利用上下解方法以及积分估计的方法得到两类在有限时间内解熄灭的结果,研究中所利用的方法是一种常用方法,可以推广到更一般的拟线性抛物方程的研究中去。

This paper deals with extinction of solution of the initial boundary value problem of quasi-linear parabolic equation ut-div[σ（｜▽u｜2）▽u]=h（x）up in a bounded convex domain of R N with N≥2.Through upper and lower solution and integral estimate method, two results of extinction of solution can be obtained. The results obtained can be extended to more general form of quasi-linear parabolic equations.