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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 1, Pages 56–70
(Mi timm1142)
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This article is cited in 1 scientific paper (total in 1 paper)
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
R. R. Gadyl'shina, S. V. Repjevskijb, E. A. Shishkinaa a Bashkir State Pedagogical University, Ufa
b Chelyabinsk State University
Abstract:
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.
Keywords:
Laplace operator; singular perturbation; small parameter; eigenvalue; asymptotics.
Received: 10.12.2014
Citation:
R. R. Gadyl'shin, S. V. Repjevskij, E. A. Shishkina, “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”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 56–70; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 76–90
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https://www.mathnet.ru/eng/timm1142 https://www.mathnet.ru/eng/timm/v21/i1/p56
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Abstract page: | 414 | Full-text PDF : | 112 | References: | 75 | First page: | 15 |
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