A. A. Kiselev, B. S. Pavlov, “The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators”, TMF, 100:3 (1994), 354–366; Theoret. and Math. Phys., 100:3 (1994), 1065

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 100, Number 3, Pages 354–366 (Mi tmf1654)

This article is cited in 11 scientific papers (total in 11 papers)

The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators

A. A. Kiselev^a, B. S. Pavlov^b

^a Saint-Petersburg State University
^b V. A. Fock Institute of Physics, Saint-Petersburg State University

Full-text PDF (1123 kB) Citations (11)

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Abstract: The model Neuman Laplacian in the system of two resonators, connected through a thin channel, is studied. The first terms of the asymptotic expansions of eigenvalues and eigenfunctions by small linking parameter are obtained. An explicit expression for resolvent is derived. The model problem is compared to a real one.

Received: 05.04.1993

English version:
Theoretical and Mathematical Physics, 1994, Volume 100, Issue 3, Pages 1065–1074
DOI: https://doi.org/10.1007/BF01018571

Bibliographic databases:

Language: Russian

Citation: A. A. Kiselev, B. S. Pavlov, “The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators”, TMF, 100:3 (1994), 354–366; Theoret. and Math. Phys., 100:3 (1994), 1065–1074

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf1654

https://www.mathnet.ru/eng/tmf/v100/i3/p354

This publication is cited in the following 11 articles:

Dozyslav B. Kuryliak, Oleksiy M. Sharabura, “Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity”, Applied Sciences, 13:14 (2023), 8517
Vorobiev A.M., “Resonance Asymptotics For Quantum Waveguides With Semitransparent Multi-Perforated Wall”, Nanosyst.-Phys. Chem. Math., 12:4 (2021), 462–471
Vorobiev A.M. Trifanova E.S. Popov I.Y., “Resonance Asymptotics For a Pair Quantum Waveguides With Common Semitransparent Perforated Wall”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 619–627
Vorobiev A.M. Bagmutov A.S. Popov I A., “On Formal Asymptotic Expansion of Resonance For Quantum Waveguide With Perforated Semitransparent Barrier”, Nanosyst.-Phys. Chem. Math., 10:4 (2019), 415–419
Dozyslav B. Kuryliak, Zinoviy Theodorovych Nazarchuk, Oksana B. Trishchuk, “AXIALLY-SYMMETRIC TM-WAVES DIFFRACTION BY SPHERE-CONICAL CAVITY”, PIER B, 73 (2017), 1
R. R. Gadyl'shin, “On the eigenvalues of a “dumb-bell with a thin handle””, Izv. Math., 69:2 (2005), 265–329
Pavlov, BS, “Possible construction of a quantum multiplexer”, Europhysics Letters, 52:2 (2000), 196
V.A. Geyler, I.Yu. Popov, S.L. Popova, “Transmission coefficient for ballistic transport through quantum resonator”, Reports on Mathematical Physics, 40:3 (1997), 531
Alexander Kiselev, “Some Examples in One-Dimensional “Geometric” Scattering on Manifolds”, Journal of Mathematical Analysis and Applications, 212:1 (1997), 263
R. R. Gadyl'shin, “On scattering by cylinder with narrow slit and with shell of finite depth”, Theoret. and Math. Phys., 106:1 (1996), 19–34
V. A. Geiler, I. Yu. Popov, “Ballistic transport in nanostructures: explicitly solvable models”, Theoret. and Math. Phys., 107:1 (1996), 427–434

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	67
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