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 Avtomat. i Telemekh., 2007, Issue 2, Pages 138–151 (Mi at946)

Systems with Distributed Parameters

The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables

Voronezh State University

Abstract: A new representation is proved of the solutions of initial boundary value problems for the equation of the form $u_{xx}(x,t)+r(x)u_{x}(x,t)-q(x)u(x,t)=u_{tt}(x,t)+\mu(x)u_{t}(x,t)$ in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the $x$ and $t$ over the given section.

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English version:
Automation and Remote Control, 2007, 68:2, 337–350

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Â. Í. Áóêîâ

Citation: V. L. Pryadiev, A. V. Pryadiev, “The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables”, Avtomat. i Telemekh., 2007, no. 2, 138–151; Autom. Remote Control, 68:2 (2007), 337–350

Citation in format AMSBIB
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\paper The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables
\jour Avtomat. i Telemekh.
\yr 2007
\issue 2
\pages 138--151
\mathnet{http://mi.mathnet.ru/at946}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2301554}
\zmath{https://zbmath.org/?q=an:1129.93021}
\transl
\jour Autom. Remote Control
\yr 2007
\vol 68
\issue 2
\pages 337--350
\crossref{https://doi.org/10.1134/S0005117907020142}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947180116}

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This publication is cited in the following articles:
1. Pryadiev V.L., “Integral operator inverting the initial-boundary value problem for a hyperbolic equation on a geometric graph”, Doklady Mathematics, 78:3 (2008), 920–922
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