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：1
|
作者：
Gadyl'shin, R. R. [1 ]
Rep'evskii, S. V. [2 ]
Shishkina, E. A. [1 ]
机构：
[1] Bashkir State Pedag Univ, Ul Oktyabrskoi Revolyutsii 3A, Ufa 450000, Russia
[2] Chelyabinsk State Univ, Ul Br Kashirinykh 129, Chelyabinsk 454001, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 292卷
基金：
俄罗斯基础研究基金会;
关键词：
Laplace operator; singular perturbation; small parameter; eigenvalue; asymptotics;
D O I：
10.1134/S0081543816020073
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 the circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. A complete asymptotic expansion with respect to a parameter (the length of the small arc) is constructed for an eigenvalue of this problem that converges to a double eigenvalue of the Neumann problem.
引用
收藏
页码：S76 / S90
页数：15
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