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Nonlocal Problem for Fourth-Order Loaded Hyperbolic Equations

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Abstract

We consider the nonlocal problem for fourth-order loaded hyperbolic equations with two independent variables. This problem is reduced to an equivalent problem consisting of a nonlocal problem for a system of loaded hyperbolic equations of the second order with functional parameters and integral relations by the method of introducing new unknown functions. Algorithms for finding solution to the equivalent problem are proposed. Conditions for well-posedness to the nonlocal problem for the system of loaded hyperbolic equations of the second order are obtained. Conditions for the existence of a unique classical solution to the nonlocal problem for fourth-order loaded hyperbolic equations are established.

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ACKNOWLEDGMENTS

This work was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, project no. AP 09258829.

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Authors and Affiliations

  1. Zhubanov Aktobe Regional University, 030000, Aktobe, Kazakhstan

    G. A. Abdikalikova

  2. Institute of Mathematics and Mathematical Modeling, 050012, Almaty, Kazakhstan

    A. T. Assanova

  3. Abai Kazakh National Pedagogical University, 050012, Almaty, Kazakhstan

    Sh. T. Shekerbekova

Authors
  1. G. A. Abdikalikova
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  2. A. T. Assanova
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  3. Sh. T. Shekerbekova
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Correspondence to G. A. Abdikalikova, A. T. Assanova or Sh. T. Shekerbekova.

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Translated by E. Seifina

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Abdikalikova, G.A., Assanova, A.T. & Shekerbekova, S.T. Nonlocal Problem for Fourth-Order Loaded Hyperbolic Equations. Russ Math. 66, 1–18 (2022). https://doi.org/10.3103/S1066369X22080011

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