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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 647–666 (Mi zvmmf486)  

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

Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination

A. Yu. Shcheglov

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

Abstract: The inverse problem of recovering a solution-dependent coefficient multiplying the lowest derivative in a hyperbolic equation is investigated. As overdetermination is required in the inverse problem, an additional condition is imposed on the solution to the equation with a fixed value of the timelike variable. Global uniqueness and local existence theorems are proved for the solution to the inverse problem. An iterative method is proposed for solving the inverse problem.

Key words: quasi-linear hyperbolic equations, inverse coefficient problem, iterative method, numerical solution.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 616–635

Bibliographic databases:

UDC: 519.633.9
Received: 24.12.2003
Revised: 10.11.2005

Citation: A. Yu. Shcheglov, “Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 647–666; Comput. Math. Math. Phys., 46:4 (2006), 616–635

Citation in format AMSBIB
\Bibitem{Shc06}
\by A.~Yu.~Shcheglov
\paper Inverse coefficient problem for a~quasilinear hyperbolic equation with final overdetermination
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 647--666
\mathnet{http://mi.mathnet.ru/zvmmf486}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260355}
\zmath{https://zbmath.org/?q=an:05200934}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 616--635
\crossref{https://doi.org/10.1134/S0965542506040099}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746043717}


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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. D. V. Churbanov, A. Yu. Shcheglov, “An iterative method for solving an inverse problem for a first-order nonlinear partial differential equation with estimates of guaranteed accuracy and the number of steps”, Comput. Math. Math. Phys., 53:2 (2013), 215–220  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
    3. Ya. T. Megraliev, B. K. Velieva, “Obratnaya kraevaya zadacha dlya linearizovannogo uravneniya Benni-Lyuka s nelokalnymi usloviyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 166–182  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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