一类具有非线性记忆的退化奇异抛物方程解的爆破  

Blow-up for a Degenerate and Singular Parabolic Equation with Nonlinear Memory

作　　者：石立新[1] 

机构地区：[1]四川农业大学数学系,四川雅安625014

出　　处：《西南大学学报（自然科学版）》2009年第11期19-22,共4页Journal of Southwest University(Natural Science Edition)

基　　金：四川省教育厅重点项目(08ZA060)

摘　　要：运用上下解方法讨论具有非线性记忆和齐次Dirichlet边界条件的退化奇异抛物方程xmut-(xrux)x=t∫0upds正解的爆破性质,得到方程解在有限时间爆破和全局存在的条件.This paper deals with the blow-up properties of the solution to the degenerate and singular parabolic equationdsx^mu1-（x^rux）x=∫0tup ds with non local memory and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution to exist globally or blow up in finite time are obtained.

关 键 词：退化奇异抛物方程 爆破 非线性记忆 

分 类 号：O175.26[理学—数学]