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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 16–22 (Mi znsl4037)  

This article is cited in 2 scientific papers (total in 3 papers)

Asymptotic behavior relative to a large parameter of the solution of the Fok–Klein–Gordon equation in the case of a discontinuous initial condition

V. M. Babich
Full-text PDF (308 kB) Citations (3)
Abstract: One considers the problem of the asymptotic behavior for $k\to+\infty$ of the solution of the Cauchy problem:
$$ u_{tt}-u_{xx}+k^2u=0;\qquad u\mid_{t=0}=\theta(x),\quad u_t\mid_{t=0}=0\ (t>0\text{ -- fixed}). $$
Here $\theta(x)$ is the Heaviside function. In the neighborhood of the characteristics $x=\pm t$ function $u(x,t)$ oscillates exceptionally fast (the wavelength is of order $k^{-2}$). Near the $t$ axis the asymptotics of $u(x,t)$ contains the Fresnel integral.
English version:
Journal of Soviet Mathematics, 1985, Volume 28, Issue 5, Pages 628–632
DOI: https://doi.org/10.1007/BF02112326
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: V. M. Babich, “Asymptotic behavior relative to a large parameter of the solution of the Fok–Klein–Gordon equation in the case of a discontinuous initial condition”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 16–22; J. Soviet Math., 28:5 (1985), 628–632
Citation in format AMSBIB
\Bibitem{Bab82}
\by V.~M.~Babich
\paper Asymptotic behavior relative to a~large parameter of the solution of the Fok--Klein--Gordon equation in the case of a~discontinuous initial condition
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~14
\serial Zap. Nauchn. Sem. LOMI
\yr 1982
\vol 115
\pages 16--22
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4037}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=660068}
\zmath{https://zbmath.org/?q=an:0562.35012|0501.35008}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 5
\pages 628--632
\crossref{https://doi.org/10.1007/BF02112326}
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  • https://www.mathnet.ru/eng/znsl/v115/p16
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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