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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1993, Volume 54, Issue 6, Pages 10–21 (Mi mz2447)

Characteristic frequencies of bodies with thin spikes. I. Convergence and estimates

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

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English version:
Mathematical Notes, 1993, 54:6, 1192–1199

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UDC: 517

Citation: R. R. Gadyl'shin, “Characteristic frequencies of bodies with thin spikes. I. Convergence and estimates”, Mat. Zametki, 54:6 (1993), 10–21; Math. Notes, 54:6 (1993), 1192–1199

Citation in format AMSBIB
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This publication is cited in the following articles:
1. R. R. Gadyl'shin, “On eigenfrequencies of bodies with thin branches. II. Asymptotics”, Math. Notes, 55:1 (1994), 14–23
2. R. R. Gadyl'shin, “Asymptotic expansion of the solutions of a singularly perturbed Dirichlet problem”, Comput. Math. Math. Phys., 36:1 (1996), 75–84
3. R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Math. Surveys, 52:1 (1997), 1–72
4. R. R. Gadyl'shin, “Characteristic frequencies of bodies with thin spikes. III. Frequency splitting”, Math. Notes, 61:4 (1997), 409–416
5. R. R. Gadyl'shin, “On the eigenvalues of a “dumb-bell with a thin handle””, Izv. Math., 69:2 (2005), 265–329
6. A. R. Bikmetov, “Asymptotics of eigenelements of boundary value problems for the Schrödinger operator with a large potential localized on a small set”, Comput. Math. Math. Phys., 46:4 (2006), 636–650
7. Comput. Math. Math. Phys., 46:1 (2006), 97–110
8. D. B. Davletov, “Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory”, Russian Math. (Iz. VUZ), 52:12 (2008), 4–12
9. D. B. Davletov, “Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity”, Comput. Math. Math. Phys., 48:10 (2008), 1811–1822
10. 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
11. 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”, Differ. Equ., 46:5 (2010), 667–680
12. S. A. Nazarov, “Waveguide with double threshold resonance at a simple threshold”, Sb. Math., 211:8 (2020), 1080–1126
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