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 Mat. Sb., 1998, Volume 189, Number 8, Pages 141–160 (Mi msb334)

Stabilization of the solutions of the wave equation in domains with non-compact boundaries

A. V. Filinovskii

N. E. Bauman Moscow State Technical University

Abstract: The asymptotic behaviour (for large values of time) of the solutions of the first mixed boundary-value problem for the wave equation in domains with non-compact, non-star-shaped boundaries is considered. Estimates with respect to the spectral parameter of the solutions of the first boundary-value problem for the Helmholtz equation are obtained.

DOI: https://doi.org/10.4213/sm334

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English version:
Sbornik: Mathematics, 1998, 189:8, 1251–1272

Bibliographic databases:

UDC: 517.956.3
MSC: Primary 35L05; Secondary 35B40

Citation: A. V. Filinovskii, “Stabilization of the solutions of the wave equation in domains with non-compact boundaries”, Mat. Sb., 189:8 (1998), 141–160; Sb. Math., 189:8 (1998), 1251–1272

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb334
• https://doi.org/10.4213/sm334
• http://mi.mathnet.ru/eng/msb/v189/i8/p141

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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. A. V. Filinovskii, “Energy decay of solutions of the first mixed problem for the wave equation in regions with noncompact boundary”, Math. Notes, 67:2 (2000), 256–260
2. Filinovskii, AV, “On the behavior of the resolvent of the first boundary value problem for the Laplace operator in domains with noncompact boundaries at small parameter values”, Doklady Mathematics, 63:3 (2001), 310
3. “Stabilization of solutions of wave equation in domains with star-shaped boundaries”, Russian Journal of Mathematical Physics, 8:4 (2001), 433–452
4. A. V. Filinovskii, “Stabilization of solutions of the first mixed problem for the wave equation in domains with non-compact boundaries”, Sb. Math., 193:9 (2002), 1349–1380
5. A. V. Filinovskii, “Stabilization of solutions to the first mixed problem for the wave equation in domains with noncompact boundaries”, Dokl. Math., 65:3 (2002), 420–424
6. A. V. Filinovskii, “Spectrum and stabilization in hyperbolic problems”, J. Math. Sci. (N. Y.), 234:4 (2018), 531–547
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