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Mat. Sb., 1996, Volume 187, Number 6, Pages 131–160 (Mi msb141)  

This article is cited in 16 scientific papers (total in 16 papers)

Stabilization of the solutions of the wave equation in unbounded domains

A. V. Filinovskii

N. E. Bauman Moscow State Technical University

Abstract: The behaviour of the solution of the first mixed problem for the wave equation in an unbounded domain with smooth boundary is studied for large values of time. Estimates of the solution of the first boundary-value problem for the Helmholtz equation with spectral parameter in the closed upper half-plane are obtained, and uniqueness of its solution for a parameter on the real line is proved.

DOI: https://doi.org/10.4213/sm141

Full text: PDF file (388 kB)
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English version:
Sbornik: Mathematics, 1996, 187:6, 917–947

Bibliographic databases:

UDC: 517.956.3
MSC: 35L05, 35J05
Received: 07.06.1995 and 11.01.1996

Citation: A. V. Filinovskii, “Stabilization of the solutions of the wave equation in unbounded domains”, Mat. Sb., 187:6 (1996), 131–160; Sb. Math., 187:6 (1996), 917–947

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. V. V. Filippov, “The equicontinuity condition for sequences of solution spaces”, Math. Notes, 61:3 (1997), 340–345  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Filinovskii, AV, “Continuity of the spectrum of the Neumann problem for second-order elliptic operators in expanding domains”, Mathematical Notes, 61:3–4 (1997), 387  mathnet  crossref  mathscinet  isi
    3. A. V. Filinovskii, “Decay of solutions of the wave equation and spectral properties of the Laplace operator in expanding domains”, Math. Notes, 63:1 (1998), 140–142  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. V. Filinovskii, “Stabilization of the solutions of the wave equation in domains with non-compact boundaries”, Sb. Math., 189:8 (1998), 1251–1272  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Filinovskii, AV, “The decay of solutions of the first initial boundary value problem for the wave equation in the domains with infinite boundaries”, Doklady Akademii Nauk, 360:6 (1998), 736  mathnet  mathscinet  isi
    6. Filinovskii, AV, “Stabilization of solutions of the first mixed problem for wave equation in the domains with infinite boundaries”, Doklady Akademii Nauk, 366:2 (1999), 167  mathnet  mathscinet  zmath  isi
    7. 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
    8. Filinovskii, AV, “Stabilization of solutions of wave equation in domains with star-shaped boundaries”, Russian Journal of Mathematical Physics, 8:4 (2001), 433  mathscinet  zmath  isi  elib
    9. Filinovskii, AV, “Stabilization of solutions to the wave equation in domains with star-shaped boundaries”, Doklady Mathematics, 64:1 (2001), 71  zmath  isi  elib
    10. 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
    11. 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
    12. Filinovskii, AV, “Stabilization of solutions to the first mixed problem for the wave equation in domains with noncompact boundaries”, Doklady Mathematics, 65:3 (2002), 420  zmath  isi  elib
    13. A. V. Filinovskii, “On the decay rate of solutions of the wave equation in domains with star-shaped boundaries”, J. Math. Sci. (N. Y.), 143:4 (2007), 3429–3440  mathnet  crossref  mathscinet  elib
    14. Filinovskii A.V., “The spectrum of weighted Laplace operator in unbounded domains”, Doklady Mathematics, 83:1 (2011), 63–67  crossref  mathscinet  zmath  isi  elib  elib  scopus
    15. A. V. Filinovskii, “Hyperbolic equations with growing coefficients in unbounded domains”, J. Math. Sci. (N. Y.), 197:3 (2014), 435–446  mathnet  crossref  elib
    16. 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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