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Sbornik: Mathematics, 1998, Volume 189, Issue 4, Pages 503–526
DOI: https://doi.org/10.1070/sm1998v189n04ABEH000305 (Mi sm305) 		 
This article is cited in 14 scientific papers (total in 15 papers)

Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit

R. R. Gadyl'shina, A. M. Il'inb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (278 kB) Citations (15)
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DOI: https://doi.org/10.1070/sm1998v189n04ABEH000305
Abstract: The Dirichlet problem in a two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the limiting problem is constructed by means of the method of matched asymptotic expansions. It is shown that the regular perturbation theory can formally be applied in a natural way up to terms of order $\varepsilon ^2$. However, the result obtained in that way is false. The correct result can be obtained only by means of an inner asymptotic expansion.
Received: 26.05.1997
Russian version:
Matematicheskii Sbornik, 1998, Volume 189, Number 4, Pages 25–48
DOI: https://doi.org/10.4213/sm305
Bibliographic databases:
UDC: 517.956
MSC: Primary 35C20; Secondary 35J25
Language: English
Original paper language: Russian
Citation: R. R. Gadyl'shin, A. M. Il'in, “Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit”, Mat. Sb., 189:4 (1998), 25–48; Sb. Math., 189:4 (1998), 503–526
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
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    References:65
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