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Mathematics of the USSR-Sbornik, 1988, Volume 59, Issue 2, Pages 409–427
DOI: https://doi.org/10.1070/SM1988v059n02ABEH003144
(Mi sm1971)
 

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

On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation

A. K. Gushchin, V. P. Mikhailov
References:
Abstract: This paper is devoted to the study of uniform quasiasymptotics of the solution of the second mixed problem in $(0,+\infty)\times\Omega$, $\Omega\in\mathbf R_n$, and of the Cauchy problem $(\Omega=\mathbf R_n)$ for the linear hyperbolic equation
$$ u_{tt}-\sum_{i,j=1}^n(a_{ij}(x)u_{x_i})_{x_j}=f(t,x) $$
with initial conditions
$$ u|_{t=0}=\varphi(x),\qquad u_t|_{t=0}=\psi(x). $$
A criterion for the existence of quasiasymptotics of the solution of order $\alpha+2$ is established under the assumption that the function $F(t,x)=f(t,x)\theta(t)+\psi(x)\delta(t)+\varphi(x)\delta'(t)$ has quasiasymptotics of order $\alpha$ and with a certain condition of “isoperimetric type” on the class of domains $\Omega$ considered.
Bibliography: 13 titles.
Received: 21.04.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1986, Volume 131(173), Number 4(12), Pages 419–437
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35L15, 35L20, 35B40
Language: English
Original paper language: Russian
Citation: A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Mat. Sb. (N.S.), 131(173):4(12) (1986), 419–437; Math. USSR-Sb., 59:2 (1988), 409–427
Citation in format AMSBIB
\Bibitem{GusMik86}
\by A.~K.~Gushchin, V.~P.~Mikhailov
\paper On uniform quasiasymptotics of solutions of the second mixed problem for a~hyperbolic equation
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 131(173)
\issue 4(12)
\pages 419--437
\mathnet{http://mi.mathnet.ru/sm1971}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=881906}
\zmath{https://zbmath.org/?q=an:0635.35056}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 59
\issue 2
\pages 409--427
\crossref{https://doi.org/10.1070/SM1988v059n02ABEH003144}
Linking options:
  • https://www.mathnet.ru/eng/sm1971
  • https://doi.org/10.1070/SM1988v059n02ABEH003144
  • https://www.mathnet.ru/eng/sm/v173/i4/p419
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:455
    Russian version PDF:113
    English version PDF:11
    References:80
    First page:3
     
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