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Uspekhi Mat. Nauk, 1974, Volume 29, Issue 2(176), Pages 154–165 (Mi umn4360)  

This article is cited in 4 scientific papers (total in 4 papers)

Fundamental solutions and lacunae of quasihyperbolic equations

S. A. Gal'pern


Abstract: This article is devoted to a study of the behaviour of the solution to the Cauchy problem for the quasihyperbolic equation (1) (defined below in §1). For such equations, as we shall show, certain regions inside the base of the characteristic cone can turn out to be lacunae or weak lacunae (defined in §1). Next we show that each quasihyperbolic equation (1) can be regarded as the limit for some hyperbolic equation whose coefficients in the series of higher derivatives in $t$ tend to zero. We establish a connection between fundamental solutions to the Cauchy problem for both equations. The statements of the main results have been published in [1].

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English version:
Russian Mathematical Surveys, 1974, 29:2, 158–169

Bibliographic databases:

UDC: 517.9
MSC: 35A08, 35E05, 35B05, 35Lxx
Received: 14.02.1974

Citation: S. A. Gal'pern, “Fundamental solutions and lacunae of quasihyperbolic equations”, Uspekhi Mat. Nauk, 29:2(176) (1974), 154–165; Russian Math. Surveys, 29:2 (1974), 158–169

Citation in format AMSBIB
\Bibitem{Gal74}
\by S.~A.~Gal'pern
\paper Fundamental solutions and lacunae of quasihyperbolic equations
\jour Uspekhi Mat. Nauk
\yr 1974
\vol 29
\issue 2(176)
\pages 154--165
\mathnet{http://mi.mathnet.ru/umn4360}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=415051}
\zmath{https://zbmath.org/?q=an:0294.35049|0305.35064}
\transl
\jour Russian Math. Surveys
\yr 1974
\vol 29
\issue 2
\pages 158--169
\crossref{https://doi.org/10.1070/RM1974v029n02ABEH003840}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. R. Vainberg, “On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems”, Russian Math. Surveys, 30:2 (1975), 1–58  mathnet  crossref  mathscinet  zmath
    2. A. A. Lokshin, “Usloviya suschestvovaniya slabykh lakun”, UMN, 30:3(183) (1975), 165–166  mathnet  mathscinet  zmath
    3. A. A. Lokshin, “Rasprostranenie vozmuschenii ot tochechnogo istochnika, opisyvaemoe kvazigiperbolicheskim uravneniem”, UMN, 31:5(191) (1976), 243–244  mathnet  mathscinet  zmath
    4. C.H. Daros, “A fundamental solutions for transversely isotropic, piezoelectric solids under electrically irrotational approximation”, Mechanics Research Communications, 29:1 (2002), 61  crossref
  • Успехи математических наук Russian Mathematical Surveys
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