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Algebra i Analiz, 1998, Volume 10, Issue 1, Pages 3–19 (Mi aa969)  

This article is cited in 32 scientific papers (total in 32 papers)

Research Papers

On the asymptotics of eigenvalues for a periodically fixed membrane

R. R. Gadyl'shin

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

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English version:
St. Petersburg Mathematical Journal, 1999, 10:1, 1–14

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Received: 24.10.1996

Citation: R. R. Gadyl'shin, “On the asymptotics of eigenvalues for a periodically fixed membrane”, Algebra i Analiz, 10:1 (1998), 3–19; St. Petersburg Math. J., 10:1 (1999), 1–14

Citation in format AMSBIB
\by R.~R.~Gadyl'shin
\paper On the asymptotics of eigenvalues for a periodically fixed membrane
\jour Algebra i Analiz
\yr 1998
\vol 10
\issue 1
\pages 3--19
\jour St. Petersburg Math. J.
\yr 1999
\vol 10
\issue 1
\pages 1--14

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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. Gadyl'shin, RR, “On an analog of the Helmholtz resonator in the averaging theory”, Comptes Rendus de l Academie Des Sciences Serie i-Mathematique, 329:12 (1999), 1121  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Math. Notes, 70:4 (2001), 471–485  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. R. R. Gadyl'shin, “On a Model Analogue of the Helmholtz Resonator in Homogenization”, Proc. Steklov Inst. Math., 236 (2002), 70–77  mathnet  mathscinet  zmath
    4. D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. 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
    6. Borisov D.I., “On a singularly perturbed boundary value problem for the Laplacian in a cylinder”, Differential Equations, 38:8 (2002), 1140–1148  mathnet  crossref  mathscinet  zmath  isi  scopus
    7. Borisov D.I., “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady Mathematics, 65:2 (2002), 224–226  mathscinet  zmath  isi
    8. D. I. Borisov, “Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. Math., 67:6 (2003), 1101–1148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. D. I. Borisov, “Asymptotics and estimates of the convergence rate in a three-dimensional boundary-value problem with rapidly alternating boundary conditions”, Siberian Math. J., 45:2 (2004), 222–240  mathnet  crossref  mathscinet  zmath  isi  elib
    10. G. A. Chechkin, “Splitting of a multiple eigenvalue in a problem on concentrated masses”, Russian Math. Surveys, 59:4 (2004), 790–791  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. Chechkin, GA, “On the vibration of a partially fastened membrane with many 'light' concentrated masses on the boundary”, Comptes Rendus Mecanique, 332:12 (2004), 949  crossref  zmath  adsnasa  isi  scopus
    12. Gadyl'shin R.R., “On resonance scattering in the two–dimensional averaging problem”, Doklady Mathematics, 70:1 (2004), 639–643  mathscinet  zmath  isi
    13. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. M. Yu. Planida, “Asymptotics of the eigenelements of the Laplacian with singular perturbations of boundary conditions on narrow and thin sets”, Sb. Math., 196:5 (2005), 703–741  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. Chechkin, GA, “Non-periodic boundary homogenization and “light” concentrated masses”, Indiana University Mathematics Journal, 54:2 (2005), 321  crossref  mathscinet  zmath  isi  elib  scopus
    16. D. I. Borisov, “On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets”, Comput. Math. Math. Phys., 46:2 (2006), 271–281  mathnet  crossref  mathscinet  zmath  elib  elib
    17. Perez, E, “On periodic Steklov type eigenvalue problems on half-bands and the spectral homogenization problem”, Discrete and Continuous Dynamical Systems-Series B, 7:4 (2007), 859  crossref  mathscinet  zmath  isi  scopus
    18. Chechkin, GA, “On boundary-value problems for the Laplacian in bounded domains with micro inhomogeneous structure of the boundaries”, Acta Mathematica Sinica-English Series, 23:2 (2007), 237  crossref  mathscinet  zmath  isi  scopus
    19. Chechkin G.A., Koroleva Yu.O., Persson L.-E., “On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure”, Journal of Inequalities and Applications, 2007, 34138  mathscinet  zmath  isi
    20. Borisov, D, “Homogenization of the planar waveguide with frequently alternating boundary conditions”, Journal of Physics A-Mathematical and Theoretical, 42:36 (2009), 365205  crossref  mathscinet  zmath  isi  scopus
    21. Chechkin, GA, “On the Friedrichs inequality in a domain perforated aperiodically along the boundary. Homogenization procedure. Asymptotics for parabolic problems”, Russian Journal of Mathematical Physics, 16:1 (2009), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Gadyl'shin R.R., Koroleva Yu.O., Chechkin G.A., “On the convergence of solutions and eigenelements of a boundary value problem in a domain perforated along the boundary”, Differential Equations, 46:5 (2010), 667–680  crossref  mathscinet  zmath  isi  scopus
    23. V. A. Sadovnichii, A. G. Chechkina, “Ob otsenke sobstvennykh funktsii zadachi tipa Steklova s malym parametrom v sluchae predelnogo vyrozhdeniya spektra”, Ufimsk. matem. zhurn., 3:3 (2011), 127–139  mathnet  zmath
    24. Gadylshin R.R., Korolëva Yu.O., Chechkin G.A., “Ob asimptotike resheniya kraevoi zadachi v oblasti, perforirovannoi vdol granitsy”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 27, 27–36  mathscinet  elib
    25. Borisov D.I., “Ob usrednenii operatora shrëdingera v polose s bystro menyayuschimsya tipom kraevykh uslovii”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 27, 6–11  mathscinet  elib
    26. Gadyl'shin R.R., Koroleva Yu.O., Chechkin G.A., “On the Asymptotic Behavior of a Simple Eigenvalue of a Boundary Value Problem in a Domain Perforated along the Boundary”, Differ Equ, 47:6 (2011), 822–831  crossref  mathscinet  mathscinet  zmath  isi  elib  scopus
    27. D. I. Borisov, “Ob usrednenii operatora Shredingera v polose s bystro menyayuschimsya tipom kraevykh uslovii”, Vestnik ChelGU, 2011, no. 14, 6–11  mathnet
    28. R. R. Gadylshin, Yu. O. Koroleva, G. A. Chechkin, “Ob asimptotike resheniya kraevoi zadachi v oblasti, perforirovannoi vdol granitsy”, Vestnik ChelGU, 2011, no. 14, 27–36  mathnet
    29. Borisov D. Bunoiu R. Cardone G., “Waveguide with Non-Periodically Alternating Dirichlet and Robin Conditions: Homogenization and Asymptotics”, Z. Angew. Math. Phys., 64:3 (2013), 439–472  crossref  mathscinet  zmath  isi  elib  scopus
    30. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    31. A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklovtype boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29  mathnet
    32. 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  crossref  mathscinet  zmath  isi
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