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 Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 6, Pages 1332–1375 (Mi izv2364)

On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients

B. A. Plamenevskii

Abstract: A system of differential equations on the semiaxis $T<t<+\infty$ is considered with operator coefficients in a Hilbert space. The coefficients of the system depend on $t$ and for $t\to+\infty$ are stabilized in a certain sense. The spectrum of the limit operator consists of normal eigenvalues and is contained inside a certain double angle with opening less than $\pi$ which contains the imaginary axis. Asymptotic formulas are derived for the solution, and the contribution which a multiple eigenvalue of the limiting operator pencil makes to the asymptotic expressions is investigated.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:6, 1327–1370

Bibliographic databases:

UDC: 517.9
MSC: 35R20, 35B40

Citation: B. A. Plamenevskii, “On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 37:6 (1973), 1332–1375; Math. USSR-Izv., 7:6 (1973), 1327–1370

Citation in format AMSBIB
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\by B.~A.~Plamenevskii
\paper On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 6
\pages 1332--1375
\mathnet{http://mi.mathnet.ru/izv2364}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=372656}
\zmath{https://zbmath.org/?q=an:0285.35029}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 6
\pages 1327--1370
\crossref{https://doi.org/10.1070/IM1973v007n06ABEH002089}

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. A. Nazarov, “Elliptic boundary value problems with periodic coefficients in a cylinder”, Math. USSR-Izv., 18:1 (1982), 89–98
2. S. A. Nazarov, “Asymptotic of a solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain”, Russian Acad. Sci. Izv. Math., 44:1 (1995), 91–118
3. Vladimir Rabinovich, Bert-Wolfgang Schulze, Nikolai Tarkhanov, “A Calculus of Boundary Value Problems in Domains with Non-Lipschitz Singula Points”, Math Nachr, 215:1 (2000), 115
4. Ya. Rebahi, “Asymptotics of Sol tions of Differential Equations on Manifolds with Cusps”, Math Nachr, 236:1 (2002), 161
5. S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807
6. F. L. Bakharev, S. A. Nazarov, “On the structure of the spectrum for the elasticity problem in a body with a supersharp spike”, Siberian Math. J., 50:4 (2009), 587–595
7. Nazarov S.A. Sokolowski J. Taskinen J., “Neumann Laplacian on a Domain with Tangential Components in the Boundary”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 34:1 (2009), 131–143
8. Nazarov S.A. Taskinen J., “Spectral Anomalies of the Robin Laplacian in Non-Lipschitz Domains”, J. Math. Sci.-Univ. Tokyo, 20:1 (2013), 27–90
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