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Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains
Kim, Tujin1; Cao, Daomin2,3
2018-09-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume265Issue:6Pages:2648-2670
AbstractIn 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.
KeywordParabolic equation Non-cylindrical domain Mixed boundary condition Existence
DOI10.1016/j.jde.2018.04.046
Language英语
Funding ProjectTWAS 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000432947800010
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30409
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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