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 Mat. Sb. (N.S.), 1984, Volume 123(165), Number 3, Pages 291–316 (Mi msb2023)

On stabilization of the solution of the third mixed problem for the wave equation in a cylindrical domain

V. M. Favorin

Abstract: Necessary and sufficient conditions are obtained for stabilization as $t\to\infty$ of the solution of the third mixed problem for the wave equation in the exterior of an infinite closed cylindrical surface in space variables, in the presence of an influx of energy into the region through the boundary $(\frac{\partial u}{\partial n}+g(x)u|_{\partial\Omega}=0$, $g(x)$ of arbitrary sign$)$. An asymptotic expansion as $t\to\infty$ is established for the solution.
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English version:
Mathematics of the USSR-Sbornik, 1985, 51:2, 287–314

Bibliographic databases:

UDC: 517.9
MSC: 35L15, 35L20, 35B40, 35B30

Citation: V. M. Favorin, “On stabilization of the solution of the third mixed problem for the wave equation in a cylindrical domain”, Mat. Sb. (N.S.), 123(165):3 (1984), 291–316; Math. USSR-Sb., 51:2 (1985), 287–314

Citation in format AMSBIB
\Bibitem{Fav84} \by V.~M.~Favorin \paper On stabilization of the solution of the third mixed problem for the wave equation in a~cylindrical domain \jour Mat. Sb. (N.S.) \yr 1984 \vol 123(165) \issue 3 \pages 291--316 \mathnet{http://mi.mathnet.ru/msb2023} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=735709} \zmath{https://zbmath.org/?q=an:0589.35072} \transl \jour Math. USSR-Sb. \yr 1985 \vol 51 \issue 2 \pages 287--314 \crossref{https://doi.org/10.1070/SM1985v051n02ABEH002861}