COMPLETE ASYMPTOTIC EXPANSIONS FOR EIGENVALUES OF DIRICHLET LAPLACIAN IN THIN THREE-DIMENSIONAL RODS

被引：20

作者：

Borisov, Denis ^{[1
]}

Cardone, Giuseppe ^{[2
]}

机构：

[1] Bashkir State Pedag Univ, Ufa 450000, Russia

[2] Univ Sannio, Dept Engn, I-82100 Benevento, Italy

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2011年 / 17卷 / 03期

关键词：

Thin rod; Dirichlet Laplacian; eigenvalue; asymptotics; WAVE-GUIDES; EIGENFUNCTIONS; CURVATURE; SPECTRUM; STRIP;

D O I：

10.1051/cocv/2010028

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：887 / 908

页数：22

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