Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
Analysis of PDEs
2012-02-01 v2 Spectral Theory
Abstract
We consider Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions associated with these first eigenvalues.
Keywords
Cite
@article{arxiv.0910.3907,
title = {Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods},
author = {D. Borisov and G. Cardone},
journal= {arXiv preprint arXiv:0910.3907},
year = {2012}
}