一类非线性蜕化抛物型方程的全局解的存在性和光滑性

GLOBAL EXISTENCE AND REGULARITY PROPERTIESFOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATION

本文主要考虑(E1)的全局解存在性和光滑性问题。主要结果:在(E1)的假设下,α<p-2和u_0∈L^p(Ω),那么,(E1)有一个全局解存在,且解满足:对任ε>0。有essup|u|≤c(T,||u_0||p) Q_(T,z)其中Q_(T,ε)=Ω_ε×(ε,T),Ω_ε={x∈Ω|dist{x,?Ω}>ε}。

This paper is concerned with global existence and regularity properties for(E1). The main results are: if α<p-2 and u_n∈L^p(Ω), (E1)admits a global solution, which satisfies: essup|u|≤c (T, ‖u_0‖_p) for any ε>0, where Q_T,ε Q_T,ε=Ω_ε×(ε,T), Ω_ε={x∈Ω|dist{x,?Ω}>ε}.