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

This article is cited in 6 scientific papers (total in 6 papers)

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
Received: 20.11.1997

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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    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathscinet  zmath  isi  elib
    3. “Stabilization of solutions of wave equation in domains with star-shaped boundaries”, Russian Journal of Mathematical Physics, 8:4 (2001), 433–452  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  mathscinet  zmath  isi  elib
    6. A. V. Filinovskii, “Spectrum and stabilization in hyperbolic problems”, J. Math. Sci. (N. Y.), 234:4 (2018), 531–547  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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