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Heat Equation with Memory in Anisotropic and Non-Homogeneous Media

文献类型：期刊论文

作者Yong, Jiongmin1; Zhang, Xu2,3
刊名ACTA MATHEMATICA SINICA-ENGLISH SERIES
出版日期2011-02-01
卷号27期号:2页码:219-254
关键词Heat equation with memory anisotropic and non-homogeneous media well-posedness propagation speed
ISSN号1439-8516
DOI10.1007/s10114-010-0077-1
英文摘要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.
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
语种英语
WOS记录号WOS:000286122700001
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/12359]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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