This article is cited in 35 scientific papers (total in 35 papers)
On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems
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→∞.
Bibliography: 11 titles.
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”, Math. USSR-Sb., 21:2 (1973), 221–239
\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 Math. USSR-Sb.
\yr 1973
\vol 21
\issue 2
\pages 221--239
\mathnet{http://mi.mathnet.ru/eng/sm3345}
\crossref{https://doi.org/10.1070/SM1973v021n02ABEH002014}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=346319}
\zmath{https://zbmath.org/?q=an:0294.35031}
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https://doi.org/10.1070/SM1973v021n02ABEH002014
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This publication is cited in the following 35 articles:
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Lassaad Aloui, Slim Ibrahim, Moez Khenissi, “Energy decay for linear dissipative wave equations in exterior domains”, Journal of Differential Equations, 2015
Dispersion Decay and Scattering Theory, 2012, 167
E Lakshtanov, B Vainberg, “Resonance regimes of scattering by small bodies with impedance boundary conditions”, J Phys A Math Theor, 43:41 (2010), 415205
Lassaad Aloui, Moez Khenissi, “Stabilization of Schrödinger equation in exterior domains”, ESAIM COCV, 13:3 (2007), 570
Mishio Kawashita, Wakako Kawashita, “Analyticity of the resolvent for elastic waves in a perturbed isotropic half space”, Math Nachr, 278:10 (2005), 1163
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
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
Michael Melgaard, “Spectral Properties at a Threshold for Two-Channel Hamiltonians I. Abstract Theory”, Journal of Mathematical Analysis and Applications, 256:1 (2001), 281
ARNE JENSEN, GHEORGHE NENCIU, “A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS”, Rev. Math. Phys, 13:06 (2001), 717
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
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
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