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→∞, we determine the asymptotic behaviour of solutions as t→∞. For the corresponding stationary problem we obtain the short-wave asymptotic behaviour of solutions for real and complex frequencies.
Citation:
B. R. Vainberg, “On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t→∞ of solutions of non-stationary problems”, Russian Math. Surveys, 30:2 (1975), 1–58
\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 Russian Math. Surveys
\yr 1975
\vol 30
\issue 2
\pages 1--58
\mathnet{http://mi.mathnet.ru/eng/rm3983}
\crossref{https://doi.org/10.1070/RM1975v030n02ABEH001406}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=415085}
\zmath{https://zbmath.org/?q=an:0308.35011|0318.35006}
Linking options:
https://www.mathnet.ru/eng/rm3983
https://doi.org/10.1070/RM1975v030n02ABEH001406
https://www.mathnet.ru/eng/rm/v30/i2/p3
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