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Matematicheskie Zametki, 2020, Volume 108, Issue 1, Pages 3–16
DOI: https://doi.org/10.4213/mzm12514 (Mi mzm12514) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

A. T. Assanovaa, Zh. S. Tokmurzinb

a Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan
b Aktobe State University after K. Zhubanov
Full-text PDF (531 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm12514
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.
Keywords: system of fourth-order hyperbolic equations, initial boundary-value problem, hyperbolic-type integro-differential equation, nonlocal problem, solvability.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05131220
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan under grant AP05131220.
Received: 19.07.2019
Revised: 14.01.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 1, Pages 3–14
DOI: https://doi.org/10.1134/S0001434620070019
Bibliographic databases:
Document Type: Article
UDC: 517.968.7
Language: Russian
Citation: A. T. Assanova, Zh. S. Tokmurzin, “An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations”, Mat. Zametki, 108:1 (2020), 3–16; Math. Notes, 108:1 (2020), 3–14
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    1. Anar Assanova, Askarbek Imanchiyev, “A nonlocal problem with multipoint conditions for partial differential equations of higher order”, Filomat, 38:1 (2024), 295  crossref
    2. D. A. Tursunov, K. G. Kozhobekov, A. O. Mamytov, B. E. Matieva, “Solvability of One Class of Inverse Problem for Partial Differential Equations”, Lobachevskii J Math, 45:7 (2024), 3453  crossref
    3. D. A. Tursunov, K. G. Kozhobekov, A. O. Mamytov, E. A. Tursunov, “The Inverse Problem of Recovering the Kernel and the Right-Hand Side of a Fifth Order Integro-Differential Equation”, Lobachevskii J Math, 45:10 (2024), 5295  crossref
    4. Yu. P. Apakov, S. M. Mamajanov, “Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one”, Russian Math. (Iz. VUZ), 66:4 (2022), 1–11  mathnet  crossref  crossref
    5. G. A. Abdikalikova, A. T. Assanova, Sh. T. Shekerbekova, “A nonlocal problem for fourth-order loaded hyperbolic equations”, Russian Math. (Iz. VUZ), 66:8 (2022), 1–18  mathnet  crossref  crossref  mathscinet
    6. N. T. Orumbayeva, T. D. Tokmagambetova, “On One Solution of the Boundary Value Problem for a Pseudohyperbolic Equation of Fourth Order”, Lobachevskii J Math, 42:15 (2021), 3705  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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