高阶非线性退化拋物型方程的初边值问题

The Initial-boundary Value Problem for High Order Nonlinear Degenerate Parabolic Equation

本文讨论了高阶非线性退化方程■都为非负常数)的两类初边值问题全局解的存在性(Blow—up)。

In this paper we consider the initial-boundary value problems of the form By using Galerkin's method,We obtain the following results: (1)if p>2+(,the problem(I)has global(nonnegative)solutions whenever initial functions u_0(x)(are nonnegative and)belong to Sobolev space w(2/0),P(Ω). (2) if p,for sufficiently small(nonnegative)initial function u_0(x),the problem(I)has a global(nonnegative)solution.If u_0(x) is nonnegative and large enough,the solutions blows up in a finite time.