Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion

doi:10.1016/j.jde.2020.07.007

CSpace

	Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion
	Cui, Jianbo 1; Hong, Jialin 2,3
	2020-11-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	269 期号:11 页码:10143-10180
摘要	In this article, we consider the absolute continuity and numerical approximation of the solution of the stochastic Cahn-Hilliard equation with unbounded noise diffusion. We first obtain the Holder continuity and Malliavin differentiability of the solution of the stochastic Cahn-Hilliard equation by using the strong convergence of the spectral Gakerkin approximation. Then we prove the existence and strict positivity of the density function of the law of the exact solution for the stochastic Cahn-Hilliard equation with sublinear growth diffusion coefficient, which fills a gap for the existed result when the diffusion coefficient satisfies a growth condition of order 1/3 < alpha < 1. To approximate the density function of the exact solution, we propose a full discretization based on the spatial spectral Galerkin approximation and the temporal drift implicit Euler scheme. Furthermore, a general framework for deriving the strong convergence rate of the full discretization is developed based on the variation approach and the factorization method. Consequently, we obtain the sharp mean square convergence rates in both time and space via Sobolev interpolation inequalities and semigroup theories. To the best of our knowledge, this is the first result on the convergence rate of full discretizations for the considered equation. (C) 2020 Elsevier Inc. All rights reserved.
关键词	Stochastic Cahn-Hilliard equation Unbounded noise diffusion Malliavin calculus Numerical approximation Strong convergence rate
DOI	10.1016/j.jde.2020.07.007
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000575391800038
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/52291
专题	中国科学院数学与系统科学研究院
通讯作者	Cui, Jianbo
作者单位	1.Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cui, Jianbo,Hong, Jialin. Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2020,269(11):10143-10180.
APA	Cui, Jianbo,&Hong, Jialin.(2020).Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion.JOURNAL OF DIFFERENTIAL EQUATIONS,269(11),10143-10180.
MLA	Cui, Jianbo,et al."Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion".JOURNAL OF DIFFERENTIAL EQUATIONS 269.11(2020):10143-10180.