Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods

Details Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods

2009-10-20

arxiv.org/abs/0910.3907v2

ESAIM: Control, Optimisation, and Calculus of Variation. 2011. V. 17. No. 3. P. 887-908

Mathematics

Analysis of PDEs

Scientific paper

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.

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