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 Mat. Sb. (N.S.), 1986, Volume 129(171), Number 2, Pages 232–251 (Mi msb1818)

On uniform quasistabilization of solutions of the second mixed problem for a second-order hyperbolic equation

Yu. A. Mikhailov

Abstract: The problem
is considered in the cylindrical region $\Omega\times(0,+\infty)$.
A criterion for uniform stabilization (with respect to $x$ in $\Omega$) of the mean over $t$ of order $\alpha$, $\alpha>[n/2]+1$, of the solution $u(x,t)$ of this problem is proved for a rather broad class of unbounded domains $\Omega\subset\mathbf R^n$ (determined by conditions of isoperimetric type).
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 57:1, 243–262

Bibliographic databases:

UDC: 517.9
MSC: 35L20, 35B40

Citation: Yu. A. Mikhailov, “On uniform quasistabilization of solutions of the second mixed problem for a second-order hyperbolic equation”, Mat. Sb. (N.S.), 129(171):2 (1986), 232–251; Math. USSR-Sb., 57:1 (1987), 243–262

Citation in format AMSBIB
\Bibitem{Mik86} \by Yu.~A.~Mikhailov \paper On uniform quasistabilization of solutions of the second mixed problem for a~second-order hyperbolic equation \jour Mat. Sb. (N.S.) \yr 1986 \vol 129(171) \issue 2 \pages 232--251 \mathnet{http://mi.mathnet.ru/msb1818} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=838498} \zmath{https://zbmath.org/?q=an:0628.35055} \transl \jour Math. USSR-Sb. \yr 1987 \vol 57 \issue 1 \pages 243--262 \crossref{https://doi.org/10.1070/SM1987v057n01ABEH003067} 

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This publication is cited in the following articles:
1. A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Math. USSR-Sb., 59:2 (1988), 409–427
2. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371
3. V. Zh. Dumanyan, “On the uniform quasiasymptotics of the solutions of hyperbolic equations”, Math. USSR-Sb., 70:1 (1991), 109–128
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