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

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
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

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
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
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