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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 1(313), Pages 3–76 (Mi umn806)  

This article is cited in 25 scientific papers (total in 25 papers)

Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator

R. R. Gadyl'shin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm806

Full text: PDF file (664 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:1, 1–72

Bibliographic databases:

UDC: 517.9
MSC: 35J05, 35J45
Received: 18.09.1995

Citation: R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Uspekhi Mat. Nauk, 52:1(313) (1997), 3–76; Russian Math. Surveys, 52:1 (1997), 1–72

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pershenko, OS, “Nonlinear zero-range potential model for the scattering of sound intensity by a Helmholtz resonator”, Technical Physics Letters, 25:6 (1999), 492  crossref  adsnasa  isi  elib  scopus  scopus
    2. R. R. Gadyl'shin, “Resonator systems”, Izv. Math., 64:3 (2000), 487–529  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. R. R. Gadyl'shin, “On the Dirichlet problem for the Helmholtz equation on the plane with boundary conditions on an almost closed curve”, Sb. Math., 191:6 (2000), 821–848  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. R. R. Gadyl'shin, “Analogues of the Helmholtz resonator in homogenization theory”, Sb. Math., 193:11 (2002), 1611–1638  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Nazarov, SA, “Asymptotic analysis of shape functionals”, Journal de Mathematiques Pures et Appliquees, 82:2 (2003), 125  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. M. Yu. Planida, “Asymptotics of eigenvalues for a cylinder that is heat-insulated on a narrow strip”, Comput. Math. Math. Phys., 43:3 (2003), 403–413  mathnet  mathscinet  zmath
    7. Gortinskaya L.V., Popov I.Y., Tesovskaya E.S., “Laterally coupled waveguides with Neumann boundary condition: formal asymptotic expansions”, International Seminar Day on Diffraction' 2003, Proceedings, 2003, 52–59  crossref  mathscinet  isi  scopus  scopus
    8. Gadyl'shin, RR, “On regular and singular perturbations of acoustic and quantum waveguides”, Comptes Rendus Mecanique, 332:8 (2004), 647  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    9. Ammari, H, “Splitting of resonant and scattering frequencies under shape deformation”, Journal of Differential Equations, 202:2 (2004), 231  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    10. Chechkin, GA, “On boundary-value problems for the Laplacian in bounded and in unbounded domains with perforated boundaries”, Journal of Differential Equations, 216:2 (2005), 502  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    11. Planida, MY, “Singular perturbation of the Dirichlet problem in an infinite cylinder”, Doklady Mathematics, 71:3 (2005), 466  mathscinet  isi  elib
    12. Golowich, SE, “Scattering resonances of microstructures and homogenization theory”, Multiscale Modeling & Simulation, 3:3 (2005), 477  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. I. Yu. Popov, E. S. Tesovskaya, “Electron in a multilayered magnetic structure: resonance asymptotics”, Theoret. and Math. Phys., 146:3 (2006), 361–372  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. G. A. Chechkin, “Homogenization of solutions to problems for the Laplace operator in unbounded domains with many concentrated masses on the boundary”, Journal of Mathematical Sciences (New York), 139:1 (2006), 6351  crossref  mathscinet  zmath  elib  scopus  scopus
    15. Gortinskaya, L, “Electronic transport in the multilayers with very thin magnetic layers”, Physica E-Low-Dimensional Systems & Nanostructures, 36:1 (2007), 12  crossref  adsnasa  isi  elib  scopus  scopus
    16. Trifanova, ES, “Resonance phenomena in curved quantum waveguides coupled via windows”, Technical Physics Letters, 35:2 (2009), 180  crossref  adsnasa  isi  elib  scopus  scopus
    17. Gadyl'shin R.R., “On Regular and Singular Perturbations of the Eigenelements of the Laplacian”, Analytic Methods, Integral Methods in Science and Engineering, 1, 2010, 135–148  crossref  mathscinet  zmath  isi
    18. Habib Ammari, Hai Zhang, “A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators”, Commun. Math. Phys, 2015  crossref  mathscinet  isi  scopus  scopus
    19. Vorobiev A.M., Popov I.Yu., “Model of Quantum Dot and Resonant States For the Helmholtz Resonator”, 2Nd International School and Conference Saint-Petersburg Open on Optoelectronics, Photonics, Engineering and Nanostructures (Spbopen2015), Journal of Physics Conference Series, 643, IOP Publishing Ltd, 2015, 012097  crossref  isi  scopus  scopus
    20. Popov I.Yu., “Resonance States Completeness For a Model of the Helmholtz Resonator With Line-Like Window”, Appl. Math. E-Notes, 17 (2017), 157–163  mathscinet  isi
    21. Popov A.I., Popov I.Y., Gerasimov D.A., “Resonance State Completeness Problem For Quantum Graph”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 390002-1  crossref  isi  scopus  scopus
    22. Gerasimov D.A., Popov I.Y., “Completeness of Resonance States For Quantum Graph With Two Semi-Infinite Edges”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 996–1010  crossref  mathscinet  zmath  isi  scopus
    23. Gerasimov D., Popov I., Blinova I., Popov A., “Incompleteness of Resonance States For Quantum Ring With Two Semi-Infinite Edges”, Anal. Math. Phys., 9:3 (2019), 1287–1302  crossref  isi
    24. 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  crossref  isi
    25. Blinova V I., Popov I.Y., Popov I A., “Resonance States Completeness For Relativistic Particle on a Sphere With Two Semi-Infinite Lines Attached”, J. King Saud Univ. Sci., 32:1 (2020), 836–841  crossref  isi
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