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 Uspekhi Mat. Nauk, 1969, Volume 24, Issue 3(147), Pages 91–156 (Mi umn5497)

The principle of limit amplitude

D. M. Èidus

Abstract: The paper deals with the asymptotic behaviour (as $t\to\infty$) of the solutions of some non-stationary problems in mathematical physics. The main aim of the paper is to clarify conditions under which stationary oscillations can be obtained from non-stationary ones in the limit $t\to\infty$. We study the case of an elliptic self-adjoint second order operator acting in an infinite domain with a finite boundary. We also discuss some higher order operators, as well as the Laplace operator in a domain of special type with an infinite boundary.

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English version:
Russian Mathematical Surveys, 1969, 24:3, 97–167

Bibliographic databases:

UDC: 517.9+517.4
MSC: 47F05, 47A05, 47B25

Citation: D. M. Èidus, “The principle of limit amplitude”, Uspekhi Mat. Nauk, 24:3(147) (1969), 91–156; Russian Math. Surveys, 24:3 (1969), 97–167

Citation in format AMSBIB
\Bibitem{Eid69} \by D.~M.~\Eidus \paper The principle of limit amplitude \jour Uspekhi Mat. Nauk \yr 1969 \vol 24 \issue 3(147) \pages 91--156 \mathnet{http://mi.mathnet.ru/umn5497} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=601072} \zmath{https://zbmath.org/?q=an:0197.08102} \transl \jour Russian Math. Surveys \yr 1969 \vol 24 \issue 3 \pages 97--167 \crossref{https://doi.org/10.1070/RM1969v024n03ABEH001348} `

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