Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

doi:10.1007/s00220-007-0301-8

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	Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions
	Wang, Wei ; Duan, Jinqiao
	2007-10-01
发表期刊	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
卷号	275 期号:1 页码:163-186
摘要	A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with a static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.
DOI	10.1007/s00220-007-0301-8
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000248810200005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5099
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Wei
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China 2.IIT, Dept Appl Math, Chicago, IL 60616 USA 3.Ennio De Giorgi Ctr Math Res, Pisa, Italy
推荐引用方式 GB/T 7714	Wang, Wei,Duan, Jinqiao. Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2007,275(1):163-186.
APA	Wang, Wei,&Duan, Jinqiao.(2007).Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions.COMMUNICATIONS IN MATHEMATICAL PHYSICS,275(1),163-186.
MLA	Wang, Wei,et al."Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions".COMMUNICATIONS IN MATHEMATICAL PHYSICS 275.1(2007):163-186.