Solutions of Navier equations and their representation structure

doi:10.1016/j.aam.2009.04.004

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	Solutions of Navier equations and their representation structure
	Cao, Bintao
	2009-10-01
发表期刊	ADVANCES IN APPLIED MATHEMATICS
ISSN	0196-8858
卷号	43 期号:4 页码:331-374
摘要	Navier equations are used to describe the deformation of a homogeneous, isotropic and linear elastic medium in the absence of body forces. Mathematically, the system is a natural vector O (n, R)-invariant generalization of the classical Laplace equation. In this paper, we decompose the space of polynomial Solutions of Navier equations into a direct SLIM of irreducible O(n, R)-submodules and construct an explicit basis for each irreducible summand. Moreover, we explicitly solve the initial value problems for Navier equations and their wave-type extension-Lame equations by Fourier expansion and Xu's method of solving flag partial differential equations. Our work might be counted as a continuation of Olver's important work on the algebraic Study of elasticity in a certain sense. (C) 2009 Elsevier Inc. All rights reserved.
关键词	Navier equations Lame equations Polynomial solutions Bases Initial value problems
DOI	10.1016/j.aam.2009.04.004
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000270638900003
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7520
专题	中国科学院数学与系统科学研究院
通讯作者	Cao, Bintao
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cao, Bintao. Solutions of Navier equations and their representation structure[J]. ADVANCES IN APPLIED MATHEMATICS,2009,43(4):331-374.
APA	Cao, Bintao.(2009).Solutions of Navier equations and their representation structure.ADVANCES IN APPLIED MATHEMATICS,43(4),331-374.
MLA	Cao, Bintao."Solutions of Navier equations and their representation structure".ADVANCES IN APPLIED MATHEMATICS 43.4(2009):331-374.