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Mat. Sb. (N.S.), 1987, Volume 134(176), Number 3(11), Pages 353–374 (Mi msb2761)  

This article is cited in 2 scientific papers (total in 2 papers)

Comparison theorems for solutions of hyperbolic equations

A. K. Gushchin, V. P. Mikhailov


Abstract: This paper is devoted to the study of uniform quasiasymptotics of the solution of the second mixed problem for the uniformly hyperbolic equation
\begin{equation} \begin{gathered} p(x)u_{tt}-\sum^n_{i,j=1}(a_{ij}(x)u_{x_i})_{x_j}=f(t,x),\qquad t>0,\quad x\in\Omega,
\frac{\partial u}{\partial N} |_{\partial\Omega}=0,\quad u|_{t=0}=\varphi(x),\quad u_t|_{t=0}=\psi(x), \end{gathered} \end{equation}
where $\Omega$ is an unbounded domain in $\mathbf R_n$ which satisfies certain conditions, the main one of which is a condition of “isoperimetric” type, and $N$ is the conormal to $\partial\Omega$.
One of the results is a comparison theorem in which necessary and sufficient conditions are established for the existence of uniform quasiasymptotics of the solution of problem (1) if the uniform quasiasymptotics is known to exist for the solution of a problem differing from problem (1) only by the coefficient of the second derivative with respect to time.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 62:2, 349–371

Bibliographic databases:

UDC: 517.9
MSC: 35L20, 35B40
Received: 14.05.1987

Citation: A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Mat. Sb. (N.S.), 134(176):3(11) (1987), 353–374; Math. USSR-Sb., 62:2 (1989), 349–371

Citation in format AMSBIB
\Bibitem{GusMik87}
\by A.~K.~Gushchin, V.~P.~Mikhailov
\paper Comparison theorems for solutions of hyperbolic equations
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 134(176)
\issue 3(11)
\pages 353--374
\mathnet{http://mi.mathnet.ru/msb2761}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=922629}
\zmath{https://zbmath.org/?q=an:0678.35063}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 349--371
\crossref{https://doi.org/10.1070/SM1989v062n02ABEH003243}


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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. 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
    2. B. V. Kapitonov, “Ates of the rate of stabilization of solutions of exterior mixed problems for a class of evolution systems”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 331–359  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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