Explicit relation between the solutions of the heat and the Hermite heat equation

doi:10.1007/s00033-007-7044-4

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	Explicit relation between the solutions of the heat and the Hermite heat equation
	Li, Bang-He
刊名	ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
	2007-11-01
卷号	58 期号:6 页码:959-968
关键词	heat equation Hermite heat equation
ISSN号	0044-2275
DOI	10.1007/s00033-007-7044-4
英文摘要	There are lots of results on the solutions of the heat equation at partial derivative u/partial derivative t = Sigma(n)(i=1) =partial derivative(2)/partial derivative x(i)(2)u, but much less on those of the Hermite heat equation partial derivative U/partial derivative t = Sigma(n)(i=1) =(partial derivative(2)/partial derivative x(i)(2) -x(i)(2))U due to that its coefficients are not constant and even not bounded. In this paper we find an explicit relation between the solutions of these two equations thus all known results on the heat equation can be transferred to results on the Hermite heat equation which should be a completely new idea to study the Hermite equation. Some examples are given to show that known results on the Hermite equation are obtained easily by this method even improved. There is also a new uniqueness theorem with a very general condition for the Hermite equation which answers a question in a paper in Proc. Japan Acad. (2005).
语种	英语
出版者	BIRKHAUSER VERLAG AG
WOS记录号	WOS:000251215400004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/5197]
专题	系统科学研究所
通讯作者	Li, Bang-He
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math & Syst Mechnizat, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Li, Bang-He. Explicit relation between the solutions of the heat and the Hermite heat equation[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,2007,58(6):959-968.
APA	Li, Bang-He.(2007).Explicit relation between the solutions of the heat and the Hermite heat equation.ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,58(6),959-968.
MLA	Li, Bang-He."Explicit relation between the solutions of the heat and the Hermite heat equation".ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 58.6(2007):959-968.