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 |
DOI | 10.1016/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 |
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. |
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