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An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations

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Abstract

The initial boundary-value problem for systems of fourth-order partial differential equations with two independent variables is considered. By using a new unknown eigenfunction, the problem under consideration is reduced to an equivalent nonlocal problem for a system of second-order hyperbolic-type integro-differential equations with integral conditions. An algorithm for finding an approximate solution of the resulting equivalent problem is proposed, and its convergence is proved. Conditions for the existence of a unique classical solution of the initial boundary-value problem for systems of fourth-order differential equations are established in terms of the coefficients of the system and the boundary matrices.

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Funding

This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan under grant AP05131220.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan

    A. T. Assanova

  2. Zhubanov Aktobe Regional State University, 030000, Aktobe, Kazakhstan

    Zh. S. Tokmurzin

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  1. A. T. Assanova
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  2. Zh. S. Tokmurzin
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Correspondence to A. T. Assanova.

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Assanova, A.T., Tokmurzin, Z.S. An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations. Math Notes 108, 3–14 (2020). https://doi.org/10.1134/S0001434620070019

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  • DOI: https://doi.org/10.1134/S0001434620070019

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