Abstract
In this paper, we obtain an asymptotic expansion for the eigenvalues of the Laplace operator with zero Dirichlet conditions in tubes, i.e., in infinite bent cylinders with internal torsion under uniform contraction of their cross-sections, with respect to a small parameter characterizing the transverse dimensions of the tube. A method of reducing the problem of determining the eigenvalues to the solution of an implicit equation is proposed.
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Original Russian Text © V. V. Grushin, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 5, pp. 687–701.
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Grushin, V.V. Asymptotic behavior of eigenvalues of the Laplace operator in thin infinite tubes. Math Notes 85, 661–673 (2009). https://doi.org/10.1134/S000143460905006X
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DOI: https://doi.org/10.1134/S000143460905006X