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Inverse Problem for a First-Order Hyperbolic System with Memory

  • INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract

For a first-order hyperbolic system of integro-differential equations with a convolution-type integral term, we study the inverse problem of determining the convolution kernel. The direct problem is an initial–boundary value problem for this system on a finite interval \([0, H] \). Under some data consistency conditions, the inverse problem is reduced to a system of Volterra type integral equations. Further, the contraction mapping principle is applied to this system, and a theorem on the unique local solvability of the problem is proved for sufficiently small \(H\).

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Authors and Affiliations

  1. Bukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Bukhara, Uzbekistan

    D. K. Durdiev

  2. Bukhara State University, Bukhara, 200114, Uzbekistan

    Kh. Kh. Turdiev

Authors
  1. D. K. Durdiev
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  2. Kh. Kh. Turdiev
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Correspondence to D. K. Durdiev or Kh. Kh. Turdiev.

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Translated by V. Potapchouck

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Durdiev, D.K., Turdiev, K.K. Inverse Problem for a First-Order Hyperbolic System with Memory. Diff Equat 56, 1634–1643 (2020). https://doi.org/10.1134/S00122661200120125

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