Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains
文献类型：期刊论文
| 作者 | Kim, Tujin1; Cao, Daomin2,3
|
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2018-09-15 |
| 卷号 | 265期号:6页码:2648-2670 |
| 关键词 | Parabolic equation Non-cylindrical domain Mixed boundary condition Existence |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2018.04.046 |
| 英文摘要 | In this paper we study the existence of weak solutions to initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains U boolean OR(t is an element of(0, T)) Omega(t) x {t} of spatial-temporal space R-N x R. In the case of the linear equation, each boundary condition is given on any open subset of the boundary surface Sigma = U boolean OR(t is an element of(0, T) )partial derivative Omega(t) x {t} under a condition that the boundary portion for Dirichlet condition Sigma(0) subset of Sigma is nonempty at any time t. Due to this, it is difficult to reduce the problem to the one on a cylindrical domain by diffeomorphism of the spatial domains Omega(t). By a transformation of the unknown function and the penalty method, we connect the problem to a monotone operator equation for functions defined on the non-cylindrical domain. We are also concerned with a semilinear problem when the boundary portion for Dirichlet condition is cylindrical. (C) 2018 Published by Elsevier Inc. |
| 资助项目 | TWAS in Chinese Academy of Sciences ; UNESCO in Chinese Academy of Sciences ; AMSS in Chinese Academy of Sciences ; NSFC[11271354] ; NSFC[11331010] ; Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences[2008DP173182] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000432947800010 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/30408]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Kim, Tujin |
| 作者单位 | 1.Acad Sci, Inst Math, Pyongyang, North Korea 2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Kim, Tujin,Cao, Daomin. Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2018,265(6):2648-2670. |
| APA | Kim, Tujin,&Cao, Daomin.(2018).Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains.JOURNAL OF DIFFERENTIAL EQUATIONS,265(6),2648-2670. |
| MLA | Kim, Tujin,et al."Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains".JOURNAL OF DIFFERENTIAL EQUATIONS 265.6(2018):2648-2670. |
入库方式： OAI收割
来源：数学与系统科学研究院
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