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

This article is cited in 3 scientific papers (total in 3 papers)

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

Yu. A. Mikhailov


Abstract: The problem
\begin{gather*} u_{tt}(x,t)=\operatorname{div}_x(A(x)\nabla_xu(x,t)),\qquad x\in\Omega,\quad t>0;
\frac{\partial u}{\partial N}|_{\partial\Omega}=0;\quad u|_{t=0}=\varphi(x);\quad u_t|_{t=0}=0 \end{gather*}
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
Received: 24.04.1985

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  mathscinet  zmath
    2. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371  mathnet  crossref  mathscinet  zmath
    3. V. Zh. Dumanyan, “On the uniform quasiasymptotics of the solutions of hyperbolic equations”, Math. USSR-Sb., 70:1 (1991), 109–128  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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