This article is cited in 31 scientific papers (total in 31 papers)
Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case
Abstract:
We consider vibrations of a membrane which contains many “light” concentrated masses on the boundary. We study the asymptotic behaviour of the frequencies of eigenvibrations of the membrane as the small parameter (which characterizes the diameter and density of the concentrated masses) tends to zero. We construct asymptotic expansions of eigenelements of the corresponding problems and carefully justify these expansions.
Citation:
G. A. Chechkin, “Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case”, Izv. Math., 69:4 (2005), 805–846
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\by G.~A.~Chechkin
\paper Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many ``light'' concentrated masses situated on the boundary. Two-dimensional case
\jour Izv. Math.
\yr 2005
\vol 69
\issue 4
\pages 805--846
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Linking options:
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This publication is cited in the following 31 articles:
D. I. Borisov, A. I. Mukhametrakhimova, “Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities”, Sb. Math., 213:10 (2022), 1318–1371
Yuriy Golovaty, “Membranes with thin and heavy inclusions: Asymptotics of spectra”, ASY, 130:1-2 (2022), 23
Mel'nyk T., “Asymptotic Approximations For Eigenvalues and Eigenfunctions of a Spectral Problem in a Thin Graph-Like Junction With a Concentrated Mass in the Node”, Anal. Appl., 19:05 (2021), 875–939
Chechkina A.G. D'Apice C. De Maio U., “Operator Estimates For Elliptic Problem With Rapidly Alternating Steklov Boundary Condition”, J. Comput. Appl. Math., 376 (2020), 112802
Chechkin G.A., Chechkina T.P., “Random Homogenization in a Domain With Light Concentrated Masses”, Mathematics, 8:5 (2020), 788
Koroleva Yu., “Spectral Analysis of a Nonlinear Boundary-Value Problem in a Perforated Domain. Applications to the Friedrichs Inequality in Lp”, Diff. Equat. Appl., 8:4 (2016), 437–458
Giuseppe Cardone, Andrii Khrabustovskyi, “Neumann spectral problem in a domain with very corrugated boundary”, Journal of Differential Equations, 2015
T. A. Mel'nik, G. A. Chechkin, “Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses”, Izv. Math., 79:3 (2015), 467–511
A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklov–type boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29
Yulia Koroleva, “On the Convergence of a Nonlinear Boundary-Value Problem in a Perforated Domain”, International Journal of Differential Equations, 2015 (2015), 1
N. N. Abdullazade, G. A. Chechkin, “Perturbation of the Steklov Problem on a Small Part of the Boundary”, J Math Sci, 2014
G.A.. Chechkin, T.A.. Mel'nyk, “High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses”, Comptes Rendus Mécanique, 2014
A. R. Bikmetov, T. R. Gadyl’shin, I. Kh. Khusnullin, “Perturbation by Slender Potential of Operators Associated with Sectorial Forms”, J Math Sci, 2014
T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527
V. M. Hut, “Asymptotic Expansions of Eigenvalues and Eigenfunctions of a Vibrating System With Stiff Light-Weight Inclusions”, J Math Sci, 198:1 (2014), 13
T. A. Mel’nik, G. A. Chechkin, “On new types of vibrations of thick cascade junctions with concentrated masses”, Dokl. Math, 87:1 (2013), 102
G. A. Chechkin, T. A. Mel'nyk, “Spatial-skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses”, Math. Meth. Appl. Sci, 2013, n/a
Holovatyi Yu.D., Hut V.M., “Vibrating Systems with Rigid Light-Weight Inclusions: Asymptotics of the Spectrum and Eigenspaces”, Ukr. Math. J., 64:10 (2013), 1495–1513
G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall, “A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant”, Eurasian Math. J., 2:1 (2011), 81–103
Gregory A. Chechkin, Taras A. Mel'nyk, “Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses”, Applicable Analysis, 2011, 1
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