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Mat. Sb. (N.S.), 1983, Volume 120(162), Number 4, Pages 546–555 (Mi msb2147)  

The method of matching asymptotic expansions for the solution of a hyperbolic equation with a small parameter

T. N. Nesterova


Abstract: The author considers an initial-boundary value problem for the hyperbolic equation
$$ \varepsilon^2(u_{tt}-u_{xx})+a(x,t)u_t=f(x,t) $$
in a rectangle (here $\varepsilon$ is a small parameter and $a(x,t)\geqslant a_0>0$). It is assumed that the initial and boundary values of the function $u_\varepsilon(x,t)$ coincide at the lower corners of the rectangle. A complete asymptotic expansion of the solution in powers of $\varepsilon$ is constructed everywhere in the rectangle.
Bibliography: 5 titles.

Full text: PDF file (462 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 48:2, 541–550

Bibliographic databases:

UDC: 517.946
MSC: 35L20, 35B20
Received: 13.04.1982

Citation: T. N. Nesterova, “The method of matching asymptotic expansions for the solution of a hyperbolic equation with a small parameter”, Mat. Sb. (N.S.), 120(162):4 (1983), 546–555; Math. USSR-Sb., 48:2 (1984), 541–550

Citation in format AMSBIB
\Bibitem{Nes83}
\by T.~N.~Nesterova
\paper The method of matching asymptotic expansions for the solution of a~hyperbolic equation with a~small parameter
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 4
\pages 546--555
\mathnet{http://mi.mathnet.ru/msb2147}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=695960}
\zmath{https://zbmath.org/?q=an:0546.35038}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 541--550
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002691}


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