一类具有非线性边界条件的拟线性抛物方程解的全局存在性和爆破  

Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic System with Nonlinear Boundary Conditions

作　　者：米永生[1,2] 穆春来[2] 吴云龙[1] 

机构地区：[1]长江师范学院数学与计算机学院,重庆408100 [2]重庆大学数学与统计学院,重庆401331

出　　处：《数学年刊（A辑）》2014年第1期31-44,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11371384);重庆基础与前沿基金(No.cstc2013jcyjA0940)的资助

摘　　要：研究了一类具有非线性边界条件的拟线性方程组解的整体存在性和爆破.通过构造不同类型的上、下解并利用M-矩阵的基本性质,给出了非负解整体存在性的充要条件.借助这些新结果,给出了Fuiita型临界曲线,把最近的结果推广到了更一般的方程.This paper deals with the global existence and blow-up of solutions to a doubly degenerate parabolic system with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, the authors give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results to more general equations.

关 键 词：全局存在曲线 退化抛物方程 M-矩阵 非线性边界流 爆破 

分 类 号：O175.26[理学—数学]