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Mathematics of the USSR-Sbornik, 1975, Volume 26, Issue 3, Pages 403–426
DOI: https://doi.org/10.1070/SM1975v026n03ABEH002488
(Mi sm3660)
 

This article is cited in 5 scientific papers (total in 5 papers)

On the behaviour for large values of the time of the solution of the Cauchy problem for the equation $\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}+\alpha(x)u=0$

S. A. Laptev
References:
Abstract: We obtain an asymptotic expansion as $t\to\infty$ for the solution $u(t,x)$ of the Cauchy problem with initial functions of compact support for the equation
$$ u_{tt}-u_{xx}+(\alpha_0+\varphi(x))u=0,\qquad t>0,\quad-\infty<x<\infty, $$
where $\alpha_0=\text{const}$ and $\varphi(x)$ satisfies the following condition for some $k\geqslant1$:
$$ \int_{-\infty}^\infty|x|^k|\varphi(x)|\,dx<\infty. $$

Bibliography: 4 titles.
Received: 20.02.1975
Bibliographic databases:
UDC: 517.946
MSC: Primary 35L05, 35L15, 35B40, 34B25; Secondary 34A25
Language: English
Original paper language: Russian
Citation: S. A. Laptev, “On the behaviour for large values of the time of the solution of the Cauchy problem for the equation $\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}+\alpha(x)u=0$”, Math. USSR-Sb., 26:3 (1975), 403–426
Citation in format AMSBIB
\Bibitem{Lap75}
\by S.~A.~Laptev
\paper On~the behaviour for large values of the time of the solution of the Cauchy problem for the equation $\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}+\alpha(x)u=0$
\jour Math. USSR-Sb.
\yr 1975
\vol 26
\issue 3
\pages 403--426
\mathnet{http://mi.mathnet.ru//eng/sm3660}
\crossref{https://doi.org/10.1070/SM1975v026n03ABEH002488}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=385291}
\zmath{https://zbmath.org/?q=an:0313.35054}
Linking options:
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  • https://doi.org/10.1070/SM1975v026n03ABEH002488
  • https://www.mathnet.ru/eng/sm/v139/i3/p435
  • This publication is cited in the following 5 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:266
    Russian version PDF:111
    English version PDF:12
    References:47
     
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