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
收藏
页码：887 / 908
页数：22
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