RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Uspekhi Mat. Nauk: Year: Volume: Issue: Page: Find

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

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

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

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
\Bibitem{Gad97} \by R.~R.~Gadyl'shin \paper Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator \jour Uspekhi Mat. Nauk \yr 1997 \vol 52 \issue 1(313) \pages 3--76 \mathnet{http://mi.mathnet.ru/umn806} \crossref{https://doi.org/10.4213/rm806} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1453567} \zmath{https://zbmath.org/?q=an:0902.35025} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1997RuMaS..52....1G} \transl \jour Russian Math. Surveys \yr 1997 \vol 52 \issue 1 \pages 1--72 \crossref{https://doi.org/10.1070/RM1997v052n01ABEH001736} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XP14100001} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0031489587} 

• http://mi.mathnet.ru/eng/umn806
• https://doi.org/10.4213/rm806
• http://mi.mathnet.ru/eng/umn/v52/i1/p3

 SHARE:

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

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
2. R. R. Gadyl'shin, “Resonator systems”, Izv. Math., 64:3 (2000), 487–529
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
4. R. R. Gadyl'shin, “Analogues of the Helmholtz resonator in homogenization theory”, Sb. Math., 193:11 (2002), 1611–1638
5. Nazarov, SA, “Asymptotic analysis of shape functionals”, Journal de Mathematiques Pures et Appliquees, 82:2 (2003), 125
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
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
8. Gadyl'shin, RR, “On regular and singular perturbations of acoustic and quantum waveguides”, Comptes Rendus Mecanique, 332:8 (2004), 647
9. Ammari, H, “Splitting of resonant and scattering frequencies under shape deformation”, Journal of Differential Equations, 202:2 (2004), 231
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
11. Planida, MY, “Singular perturbation of the Dirichlet problem in an infinite cylinder”, Doklady Mathematics, 71:3 (2005), 466
12. Golowich, SE, “Scattering resonances of microstructures and homogenization theory”, Multiscale Modeling & Simulation, 3:3 (2005), 477
13. I. Yu. Popov, E. S. Tesovskaya, “Electron in a multilayered magnetic structure: resonance asymptotics”, Theoret. and Math. Phys., 146:3 (2006), 361–372
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
15. Gortinskaya, L, “Electronic transport in the multilayers with very thin magnetic layers”, Physica E-Low-Dimensional Systems & Nanostructures, 36:1 (2007), 12
16. Trifanova, ES, “Resonance phenomena in curved quantum waveguides coupled via windows”, Technical Physics Letters, 35:2 (2009), 180
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
18. Habib Ammari, Hai Zhang, “A Mathematical Theory of Super-Resolution by Using a System of Sub-Wavelength Helmholtz Resonators”, Commun. Math. Phys, 2015
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
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
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
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
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
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
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
•  Number of views: This page: 513 Full text: 186 References: 51 First page: 1