| 米永生,穆春来,吴云龙.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[J].数学年刊A辑,2014,35(1):31~44 |
| 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 Systemwith Nonlinear Boundary Conditions |
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| DOI： |
| 中文关键词: 全局存在曲线, 退化抛物方程, $M$-矩阵, 非线性边界流, 爆破 |
| 英文关键词:Global existence curve, Degenerate
parabolic systems, $M$-matrix, Nonlinear boundary flux, Blow-up |
| 基金项目:国家自然科学基金 (No.11371384)和重庆基础与前沿基金 (No.cstc2013jcyjA0940) |
| Author Name | Affiliation | E-mail | | MI Yongsheng | College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing 408100, China
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China. | miyongshen@163.com | | MU Chunlai | College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China. | clmu2005@163.com | | WU Yunlong | College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing 408100, China. | wyl518518@163.com |
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| 中文摘要: |
| 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Fujita 型临界曲线, 把最近的结果推广到了更一般的方程. |
| 英文摘要: |
| 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. |
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