On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case

被引：0

作者：

Gadylshin, R. R. ^{[1
,2
]}

Repjevskij, S. V. ^{[3
]}

Shishkina, E. A. ^{[2
]}

机构：

[1] Bashkir State Pedag Univ, Phys Mat Sci, Ufa, Russia

[2] Bashkir State Pedag Univ, Ufa, Russia

[3] Chelyabinsk State Univ, Chelyabinsk, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2015年 / 21卷 / 01期

关键词：

Laplace operator; singular perturbation; small parameter; eigenvalue; asymptotics;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A boundary-value problem of finding eigenvalues is considered for the negative Laplace operator in a disk with Neumann boundary condition on almost all circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. Complete asymptotic expansions with respect to a parameter (the length of the small arc) are constructed for an eigenvalue of this problem; the eigenvalue converges to a double eigenvalue of the Neumann problem.

引用

页码：56 / 70

页数：15

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