Dynamic behavior of a heat equation with memory

doi:10.1002/mma.1090

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	Dynamic behavior of a heat equation with memory
	Wang, Jun-Min 1; Guo, Bao-Zhu2,3 ; Fu, Meng-Yin 4
	2009-07-15
发表期刊	MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN	0170-4214
卷号	32 期号:10 页码:1287-1310
摘要	This paper addresses the spectrum-determined growth condition for a heat equation with exponential polynomial kernel memory. By introducing some new variables, the time-variant system is transformed into a time-invariant one. The detailed spectral analysis is presented. It is shown that the system demonstrates the property of hyperbolic equation that all eigenvalues approach a line that is parallel to the imaginary axis. The residual spectral set is shown to be empty and the set of continuous spectrum is exactly characterized. The main result is the spectrum-determined growth condition that is one of the most difficult problems for infinite-dimensional systems. Consequently, a strong exponential stability result is concluded. Copyright (C) 2008 John Wiley & Sons, Ltd.
关键词	heat equation spectrum asymptotic analysis stability
DOI	10.1002/mma.1090
语种	英语
资助项目	National Natural Science Foundation of China ; Program for New Century Excellent Talents in University of China ; National Research Foundation of South Africa
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000267271300005
出版者	JOHN WILEY & SONS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8311
专题	系统科学研究所
通讯作者	Wang, Jun-Min
作者单位	1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100081, Peoples R China 3.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, South Africa 4.Beijing Inst Technol, Sch Informat Sci & Technol, Beijing 100081, Peoples R China
推荐引用方式 GB/T 7714	Wang, Jun-Min,Guo, Bao-Zhu,Fu, Meng-Yin. Dynamic behavior of a heat equation with memory[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2009,32(10):1287-1310.
APA	Wang, Jun-Min,Guo, Bao-Zhu,&Fu, Meng-Yin.(2009).Dynamic behavior of a heat equation with memory.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,32(10),1287-1310.
MLA	Wang, Jun-Min,et al."Dynamic behavior of a heat equation with memory".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 32.10(2009):1287-1310.