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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 5, Pages 813–833 (Mi zvmmf468)  

This article is cited in 1 scientific paper (total in 1 paper)

A method for finding coefficients of a quasilinear hyperbolic equation

A. Yu. Shcheglov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: The inverse problem of finding the coefficients $q(s)$ and $p(s)$ in the equation $u_{tt}=a^2u_{xx}+q(u)u_t-p(u)u_x$ is investigated. As overdetermination required in the inverse setting, two additional conditions are set: a boundary condition and a condition with a fixed value of the timelike variable. An iteration method for solving the inverse problem is proposed based on an equivalent system of integral equations of the second kind. A uniqueness theorem and an existence theorem in a small domain are proved for the inverse problem to substantiate the convergence of the algorithm.

Key words: quasilinear hyperbolic equation, inverse problem for two coefficients, iteration method.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:5, 776–795

Bibliographic databases:

UDC: 519.633.9
Received: 08.10.2004

Citation: A. Yu. Shcheglov, “A method for finding coefficients of a quasilinear hyperbolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 813–833; Comput. Math. Math. Phys., 46:5 (2006), 776–795

Citation in format AMSBIB
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\by A.~Yu.~Shcheglov
\paper A~method for finding coefficients of a~quasilinear hyperbolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 5
\pages 813--833
\mathnet{http://mi.mathnet.ru/zvmmf468}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2286278}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 5
\pages 776--795
\crossref{https://doi.org/10.1134/S0965542506050058}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746040440}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tekin I. Mehraliyev Ya.T. Ismailov M.I., “Existence and Uniqueness of An Inverse Problem For Nonlinear Klein-Gordon Equation”, Math. Meth. Appl. Sci., 42:10 (2019), 3739–3753  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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