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

Abstract

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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.

How to cite

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Borisov, 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 -

References

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