Solutions of Navier equations and their representation structure
Cao, Bintao
刊名ADVANCES IN APPLIED MATHEMATICS
2009-10-01
卷号43期号:4页码:331-374
关键词Navier equations Lame equations Polynomial solutions Bases Initial value problems
ISSN号0196-8858
DOI10.1016/j.aam.2009.04.004
英文摘要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.
语种英语
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号WOS:000270638900003
内容类型期刊论文
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/7519]  
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
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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.
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