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An identification problem for a nonlinear one-dimensional wave equation

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  • We prove the existence of a spatial coefficient in front of a nonlinear term in a one-dimensional wave equation when, in addition to classical initial and boundary condition, an integral mean involving the displacement is prescribed.
    Mathematics Subject Classification: Primary: 35R30; Secondary: 35L20, 35L70.

    Citation:

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    Victor Isakov, "Inverse Problems for Partial Differential Equations," Second edition. Applied Mathematical Sciences, 127, Springer, New York, 2006.

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    Aleksey I. Prilepko, Dmitry G. Orlovsky and Igor A. Vasin, "Methods for Solving Inverse Problems in Mathematical Physics," Monographs and Textbooks in Pure and Applied Mathematics, 231, Marcel Dekker, Inc., New York, 2000.

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    Vladimir G. Romanov, "Inverse Problems of Mathematical Physics," VNU Science Press, b.v., Utrecht, 1987.

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    Vladimir G. Romanov, "Investigation Methods for Inverse Problems," Inverse and Ill-posed Problems Series. VSP, Utrecht, 2002.

    [7]

    Eugenio Sinestrari, Semilinear differential and integrodifferential equations with Hille-Yosida operators, Differential and Integral Equations, 23 (2010), 1-30.

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