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Uspekhi Mat. Nauk, 1975, Volume 30, Issue 2(182), Pages 3–55 (Mi umn3983)  

This article is cited in 60 scientific papers (total in 61 papers)

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

B. R. Vainberg


Abstract: In this paper we study the Cauchy problem and boundary-value problem of general form in the exterior of a compact set for hyperbolic operators $L$, whose coefficients depend only on $x$ and are constant near infinity. Assuming that the wave fronts of the Green's matrix for $L$ go off to infinity as $t\to\infty$, we determine the asymptotic behaviour of solutions as $t\to\infty$. For the corresponding stationary problem we obtain the short-wave asymptotic behaviour of solutions for real and complex frequencies.

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English version:
Russian Mathematical Surveys, 1975, 30:2, 1–58

Bibliographic databases:

UDC: 517.4
MSC: 35B40, 35L05, 47F05, 35Exx, 41A60
Received: 18.03.1974

Citation: 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”, Uspekhi Mat. Nauk, 30:2(182) (1975), 3–55; Russian Math. Surveys, 30:2 (1975), 1–58

Citation in format AMSBIB
\Bibitem{Vai75}
\by B.~R.~Vainberg
\paper 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
\jour Uspekhi Mat. Nauk
\yr 1975
\vol 30
\issue 2(182)
\pages 3--55
\mathnet{http://mi.mathnet.ru/umn3983}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=415085}
\zmath{https://zbmath.org/?q=an:0308.35011|0318.35006}
\transl
\jour Russian Math. Surveys
\yr 1975
\vol 30
\issue 2
\pages 1--58
\crossref{https://doi.org/10.1070/RM1975v030n02ABEH001406}


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