On solution of Lamé equations in axisymmetric domains with conical points

✍ Scribed by Boniface Nkemzi

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 134 KB
• Volume: 28
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.547

✦ Synopsis

Abstract

Partial Fourier series expansion is applied to the Dirichlet problem for the Lamé equations in axisymmetric domains $\hat{\Omega}$⊂ℝ^3^ with conical points on the rotation axis. This leads to dimension reduction of the three‐dimensional boundary value problem resulting to an infinite sequence of two‐dimensional boundary value problems on the plane meridian domain Ω~a~⊂ℝ of $\hat{\Omega}$ with solutions u~n~(n=0,1,2,…) being the Fourier coefficients of the solution û of the 3D BVP. The asymptotic behaviour of the Fourier coefficients u~n~ (n=0,1,2,…) near the angular points of the meridian domain Ω~a~ is fully described by singular vector‐functions which are related to the zeros α~n~ of some transcendental equations involving Legendre functions of the first kind. Equations which determine the values of α~n~ are given and a numerical algorithm for the computation of α~n~ is proposed with some plots of values obtained presented. The singular vector functions for the solution of the 3D BVP is obtained by Fourier synthesis. Copyright © 2004 John Wiley & Sons, Ltd