具有L^1初值的非牛顿多方渗流方程解的正性和熄灭性

Extinction and Positivity for the Non-Newtonian Polytropic Filtration Equation with L^1 Initial Value

利用比较原理和基本解证明了非牛顿多方渗流方程:ut=div(|▽um|p-2▽um)的解在初值u0(x)∈L1(Ω)及零边值条件下具有正性和熄灭性,其中m>0,p>1.

Abstract： This paper deals with the following Non-Newtonian polytropic filtration equation u/ t=div（｜△u^m｜^p-2△u^m） possessing the extinction and positivity of the solution by comparison principle and fundamental solution for m 〉0, p 〉 1 under initial value u0（x） ∈L^1 （Ω） and zero boundary value conditions.