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

Denis Borisov; Giuseppe Cardone

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 3, page 887-908
- ISSN: 1292-8119

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topBorisov, Denis, and Cardone, Giuseppe. "Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 887-908. <http://eudml.org/doc/272845>.

@article{Borisov2011,

abstract = {We consider the 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.},

author = {Borisov, Denis, Cardone, Giuseppe},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {thin rod; Dirichlet laplacian; eigenvalue; asymptotics; Dirichlet Laplacian; asymptotic expansions},

language = {eng},

number = {3},

pages = {887-908},

publisher = {EDP-Sciences},

title = {Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods},

url = {http://eudml.org/doc/272845},

volume = {17},

year = {2011},

}

TY - JOUR

AU - Borisov, Denis

AU - Cardone, Giuseppe

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2011

PB - EDP-Sciences

VL - 17

IS - 3

SP - 887

EP - 908

AB - We consider the 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.

LA - eng

KW - thin rod; Dirichlet laplacian; eigenvalue; asymptotics; Dirichlet Laplacian; asymptotic expansions

UR - http://eudml.org/doc/272845

ER -

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