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Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients

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Abstract

We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, 630090, Russia

    D. S. Anikonov

  2. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

    D. S. Konovalova

Authors
  1. D. S. Anikonov
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  2. D. S. Konovalova
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Correspondence to D. S. Anikonov.

Additional information

Russian Text © D.S. Anikonov, D.S. Konovalova, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 2, pp. 265–268.

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Anikonov, D.S., Konovalova, D.S. Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients. Diff Equat 55, 270–273 (2019). https://doi.org/10.1134/S0012266119020113

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  • DOI: https://doi.org/10.1134/S0012266119020113

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