Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains

doi:10.1016/j.jde.2018.04.046

CSpace > 应用数学研究所

	Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains
	Kim, Tujin 1; Cao, Daomin2,3
	2018-09-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	265 期号:6 页码:2648-2670
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.
关键词	Parabolic equation Non-cylindrical domain Mixed boundary condition Existence
DOI	10.1016/j.jde.2018.04.046
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000432947800010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30409
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.