2008/10/27 by Bintao Cao, Cao, Bintao
Engineering · Mathematics · Physics and Astronomy · #17B10 #17B20 #35C99 #Analysis of PDEs (math.AP) #Astrophysics (astro-ph) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Algebra (math.QA) #Representation Theory (math.RT) #astro-ph #math-ph #math.AP #math.MP #math.QA #math.RT #msc:17B10 #msc:17B20 #msc:35C99
paper · pdf · doi:10.48550/arxiv.0810.4766
44 pages
arxiv created 2008/10/27 · openalex publication_date 2008/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (field) O(n,\mbbR)-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,\mbbR)-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.