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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 2(10), Pages 224–241 (Mi msb3345)  

This article is cited in 20 scientific papers (total in 20 papers)

On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems

B. R. Vainberg


Abstract: In this paper elliptic problems in exterior domains polynomially depending on a spectral parameter $k$ are considered. These problems are obtained from a mixed problem for hyperbolic equations by substituting $k$ for $id/dt$. For such elliptic problems analytic properties of the resolvent are studied in the neighborhood of the point $k=0$, which permits, for the corresponding nonstationary problem, a complete asymptotic expansion of solutions as $t\to\infty$.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:2, 221–239

Bibliographic databases:

UDC: 517.944
MSC: 35J40, 35L30, 35B40
Received: 05.10.1972

Citation: B. R. Vainberg, “On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems”, Mat. Sb. (N.S.), 92(134):2(10) (1973), 224–241; Math. USSR-Sb., 21:2 (1973), 221–239

Citation in format AMSBIB
\Bibitem{Vai73}
\by B.~R.~Vainberg
\paper On~exterior elliptic problems polynomially depending on a~spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 2(10)
\pages 224--241
\mathnet{http://mi.mathnet.ru/msb3345}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=346319}
\zmath{https://zbmath.org/?q=an:0294.35031}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 2
\pages 221--239
\crossref{https://doi.org/10.1070/SM1973v021n02ABEH002014}


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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. B. R. Vainberg, “On a point source in an inhomogeneous medium”, Math. USSR-Sb., 23:1 (1974), 123–148  mathnet  crossref  mathscinet  zmath
    2. B. R. Vainberg, “On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems”, Russian Math. Surveys, 30:2 (1975), 1–58  mathnet  crossref  mathscinet  zmath
    3. Minoru Murata, “Asymptotic expansions in time for solutions of Schrödinger-type equations”, Journal of Functional Analysis, 49:1 (1982), 10  crossref
    4. Arne Jensen, “Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in L2(R4)”, Journal of Mathematical Analysis and Applications, 101:2 (1984), 397  crossref
    5. Daniel Eidus, “Solutions of external boundary problems for small values of the spectral parameter”, Integr equ oper theory, 9:1 (1986), 47  crossref  mathscinet  zmath  isi
    6. D Eidus, “Asymptotical expansions of solutions of linear parabolic equations as t → ∞”, Journal of Mathematical Analysis and Applications, 130:1 (1988), 155  crossref
    7. N. Weck, K. J. Witsch, “The low frequency limit of the exterior Dirichlet problem for the reduced wave equation”, Applicable Analysis, 38:1-2 (1990), 33  crossref
    8. Song Jiang, “Lp-Lq Estimates For Solutions To The Damped Plate Equation In Exterior Domains”, Results. Math, 18:3-4 (1990), 231  crossref
    9. N. Weck, K. J. witsch, “Exterior Dirichlet problem for the reduced wave equation: asymptotic analysis of low frequencies”, Communications in Partial Differential Equations, 16:2-3 (1991), 173  crossref
    10. Norbert Weck, Karl J. Witsch, “Complete Low Frequency Analysis for the Reduced Wave Equation with Variable Coefficients in Three Dimensions *”, Communications in Partial Differential Equations, 17:9-10 (1992), 1619  crossref
    11. N Weck, K.J Witsch, “Exact low frequency analysis for a class of exterior boundary value problems for the reduced wave equation in two dimensions”, Journal of Differential Equations, 100:2 (1992), 312  crossref
    12. R. Kleinman, B. Vainberg, “Full low-frequency asymptotic expansion for second-order elliptic equations in two dimensions”, Math Meth Appl Sci, 17:12 (1994), 989  crossref  mathscinet  zmath  isi
    13. Wakako Dan, “On the Low-frequency Asymptotic Expansion for some Second-order Elliptic Systems in a Two-dimensional Exterior Domain”, Math Meth Appl Sci, 19:13 (1996), 1073  crossref  mathscinet  zmath
    14. Michael Melgaard, “Spectral Properties at a Threshold for Two-Channel Hamiltonians I. Abstract Theory”, Journal of Mathematical Analysis and Applications, 256:1 (2001), 281  crossref
    15. ARNE JENSEN, GHEORGHE NENCIU, “A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS”, Rev. Math. Phys, 13:06 (2001), 717  crossref
    16. Michael Melgaard, “Spectral Properties in the Low- Energy Limit of One -Dimensional Schrödinger OperatorsH = -d2/dx2 +V. The Case 〈1,V1〉 ≠ 0”, Math Nachr, 238:1 (2002), 113  crossref  mathscinet  zmath
    17. Mishio Kawashita, Wakako Kawashita, “Analyticity of the resolvent for elastic waves in a perturbed isotropic half space”, Math Nachr, 278:10 (2005), 1163  crossref  mathscinet  zmath  isi
    18. Lassaad Aloui, Moez Khenissi, “Stabilization of Schrödinger equation in exterior domains”, ESAIM COCV, 13:3 (2007), 570  crossref  mathscinet  zmath  isi
    19. E Lakshtanov, B Vainberg, “Resonance regimes of scattering by small bodies with impedance boundary conditions”, J Phys A Math Theor, 43:41 (2010), 415205  crossref
    20. Lassaad Aloui, Slim Ibrahim, Moez Khenissi, “Energy decay for linear dissipative wave equations in exterior domains”, Journal of Differential Equations, 2015  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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