含非线性源的非牛顿渗流快扩散方程组解的熄灭性

Extinction of Solutions for the Fast Non-Newtonian Diffusion Equations with Nonlinear Sources

主要研究具有非线性源的非牛顿渗流快扩散方程组初边值问题解的熄灭性质。首先利用正则化方法,证明了该问题弱解存在唯一性结果。然后利用弱比较原理与Sobolev嵌入定理和适当的积分估计,根据非线性指数间关系的不同情形,分别给出了该问题解发生熄灭的条件。

This paper is concerned with the extinction of solutions the fast filtration equations with nonlinear sources.The authors obtain the existence and uniqueness of weak solutions to the considered problem by using the regularity method firstly.Then combining the weak comparison principle with the Sobolev embedding theorem and some estimates,they give the sufficient conditions on extinction solution for the problem with different kinds of exponents.