Asymptotics of the solution of a Dirichlet spectral problem in a junction with highly oscillating boundary

被引：13

作者：

Amirat, Youcef ^{[2
]}

Chechkin, Gregory A. ^{[3
,4
]}

Gadyl'shin, Rustem R. ^{[1
]}

机构：

[1] Bashkir State Pedag Univ, Fac Phys & Math, Dept Math Anal, Ufa 450000, Russia

[2] Univ Clermont Ferrand, CNRS, Math Lab, UMR 6620, F-63177 Aubiere, France

[3] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Differential Equat, Moscow 119991, Russia

[4] Narvik Univ Coll, N-8505 Narvik, Norway

来源：

COMPTES RENDUS MECANIQUE | 2008年 / 336卷 / 09期

关键词：

asymptotic expansion; spectral problem; oscillating boundary;

D O I：

10.1016/j.crme.2008.06.008

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a bounded domain, a part of whose boundary, depending on a small parameters, is highly oscillating; the frequency of oscillations of the boundary is of order epsilon and the amplitude is fixed. We present second-order asymptotic approximations, as epsilon -> 0, of the eigenelements in the case of simple eigenvalues of the limit problem.

引用

页码：693 / 698

页数：6

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