一类发展p-Laplacian方程的正解

Positivity for an Evolution p-Laplacian Equation

关键词:  p-Laplacian方程  发展方程  正解

Key words:  p-Laplacian equation  evolution equation  positivity

摘要:

讨论一类发展p-Laplacian方程(∂u)/(∂t)=∂/(∂x)(|(∂u^m)/(∂x)|^p-2(∂u^m)/(∂x))的初边值问题的弱解,并证明m(p-1)>1,而且t足够大时弱解是一个正解.

Abstract:

The weak solution of the initial boundary value problem of evolution p-Laplacian equation (∂u)/ (∂t)=∂/ (∂x) (| (∂u^m)/ (∂x)|^p-2 (∂u^m)/ (∂x))is discussed.It is proved that the weak solution is positive when m (p-1)>1 and t is large enough.