Heat Equation with Memory in Anisotropic and Non-Homogeneous Media

doi:10.1007/s10114-010-0077-1

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	Heat Equation with Memory in Anisotropic and Non-Homogeneous Media
	Yong, Jiongmin 1; Zhang, Xu 2,3
	2011-02-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	27 期号:2 页码:219-254
摘要	A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory, heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics.
关键词	Heat equation with memory anisotropic and non-homogeneous media well-posedness propagation speed
DOI	10.1007/s10114-010-0077-1
语种	英语
资助项目	National Natural Science Foundation of China[10831007] ; National Natural Science Foundation of China[60821091] ; National Natural Science Foundation of China[60974035] ; National Basic Research Program of China (973 Program)[2011CB808002] ; Spanish Ministry of Science and Innovation[MTM2008-03541]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000286122700001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12360
专题	中国科学院数学与系统科学研究院
通讯作者	Yong, Jiongmin
作者单位	1.Univ Cent Florida, Dept Math, Orlando, FL 32816 USA 2.Chinese Acad Sci, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China
推荐引用方式 GB/T 7714	Yong, Jiongmin,Zhang, Xu. Heat Equation with Memory in Anisotropic and Non-Homogeneous Media[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2011,27(2):219-254.
APA	Yong, Jiongmin,&Zhang, Xu.(2011).Heat Equation with Memory in Anisotropic and Non-Homogeneous Media.ACTA MATHEMATICA SINICA-ENGLISH SERIES,27(2),219-254.
MLA	Yong, Jiongmin,et al."Heat Equation with Memory in Anisotropic and Non-Homogeneous Media".ACTA MATHEMATICA SINICA-ENGLISH SERIES 27.2(2011):219-254.