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This article is cited in 5 scientific papers (total in 5 papers)
Characteristic frequencies of bodies with thin spikes. III. Frequency splitting
R. R. Gadyl'shin Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
Abstract:
The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem and obtain closed formulas for the leading asymptotic terms.
Received: 22.12.1994
Citation:
R. R. Gadyl'shin, “Characteristic frequencies of bodies with thin spikes. III. Frequency splitting”, Mat. Zametki, 61:4 (1997), 494–502; Math. Notes, 61:4 (1997), 409–416
Linking options:
https://www.mathnet.ru/eng/mzm1529https://doi.org/10.4213/mzm1529 https://www.mathnet.ru/eng/mzm/v61/i4/p494
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