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

 Algebra i Analiz: Year: Volume: Issue: Page: Find

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

Research Papers

On the asymptotics of eigenvalues for a periodically fixed membrane

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

Full text: PDF file (684 kB)

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

Bibliographic databases:

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
\Bibitem{Gad98} \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 \mathnet{http://mi.mathnet.ru/aa969} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1618345} \zmath{https://zbmath.org/?q=an:0907.35094} \transl \jour St. Petersburg Math. J. \yr 1999 \vol 10 \issue 1 \pages 1--14 

• http://mi.mathnet.ru/eng/aa969
• http://mi.mathnet.ru/eng/aa/v10/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. 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
2. D. I. Borisov, “Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian”, Math. Notes, 70:4 (2001), 471–485
3. R. R. Gadyl'shin, “On a Model Analogue of the Helmholtz Resonator in Homogenization”, Proc. Steklov Inst. Math., 236 (2002), 70–77
4. D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008
5. R. R. Gadyl'shin, “Analogues of the Helmholtz resonator in homogenization theory”, Sb. Math., 193:11 (2002), 1611–1638
6. Borisov D.I., “On a singularly perturbed boundary value problem for the Laplacian in a cylinder”, Differential Equations, 38:8 (2002), 1140–1148
7. Borisov D.I., “On a Laplacian with frequently nonperiodically alternating boundary conditions”, Doklady Mathematics, 65:2 (2002), 224–226
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
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
10. G. A. Chechkin, “Splitting of a multiple eigenvalue in a problem on concentrated masses”, Russian Math. Surveys, 59:4 (2004), 790–791
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
12. Gadyl'shin R.R., “On resonance scattering in the two–dimensional averaging problem”, Doklady Mathematics, 70:1 (2004), 639–643
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
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
15. Chechkin, GA, “Non-periodic boundary homogenization and “light” concentrated masses”, Indiana University Mathematics Journal, 54:2 (2005), 321
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
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
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
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
20. Borisov, D, “Homogenization of the planar waveguide with frequently alternating boundary conditions”, Journal of Physics A-Mathematical and Theoretical, 42:36 (2009), 365205
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
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
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
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
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
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
27. D. I. Borisov, “Ob usrednenii operatora Shredingera v polose s bystro menyayuschimsya tipom kraevykh uslovii”, Vestnik ChelGU, 2011, no. 14, 6–11
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
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
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
31. 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
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
•  Number of views: This page: 280 Full text: 105 First page: 1