Solutions of Navier Equations and Their Representation Structure

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dc.creatorCao, Bintao
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:13:35Z
dc.date.available2026-07-07T10:13:35Z
dc.descriptionNavier 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 (field) $O(n,\mbb{R})$-invariant generalization of the classical Laplace equation, which physically describes the vibration of a string. In this paper, we decompose the space of polynomial solutions of Navier equations into a direct sum of irreducible $O(n,\mbb{R})$-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--Lamé equations by Fourier expansion and Xu's method of solving flag partial differential equations.
dc.description44 pages
dc.identifierhttps://arxiv.org/abs/0810.4766
dc.identifierhttp://arxiv.org/abs/0810.4766
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172583
dc.subjectMathematical Physics
dc.subjectAstrophysics
dc.subjectAnalysis of PDEs
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B10;17B20;35C99
dc.titleSolutions of Navier Equations and Their Representation Structure
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