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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 16–22
(Mi znsl4037)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/znsl4037 https://www.mathnet.ru/eng/znsl/v115/p16
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Abstract page: | 174 | Full-text PDF : | 59 |
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