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Matematicheskie Zametki, 2023, Volume 114, Issue 2, Pages 244–259
DOI: https://doi.org/10.4213/mzm13686 (Mi mzm13686) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain

D. K. Durdievab, J. Sh. Safarovac

a V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, Tashkent
b Bukhara State University
c Tashkent University of Information Technology
Full-text PDF (579 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm13686
Abstract: The inverse problem of determining the solution and the kernel of the integral term in an inhomogeneous two-dimensional integrodifferential wave equation in a rectangular domain is considered. First, the uniqueness of the solution of the direct problem is established using the completeness of the eigenfunction system of the corresponding homogeneous Dirichlet problem for the two-dimensional Laplace operator, and the existence of a solution of the direct problem is proved. Using additional information about the solution of the direct problem, we obtain a Volterra integral equation of the second kind for the kernel of the integral term. The existence and uniqueness of a solution of this equation is proved by the contraction mapping method in the space of continuous functions with a weighted norm.
Keywords: integrodifferential equation, integral kernel, Fourier method, eigenfunctions, eigenvalues, Banach theorem.
Received: 10.08.2022
Revised: 06.01.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 2, Pages 199–211
DOI: https://doi.org/10.1134/S0001434623070210
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35R30
Language: Russian
Citation: D. K. Durdiev, J. Sh. Safarov, J. Sh. Safarov, “Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain”, Mat. Zametki, 114:2 (2023), 244–259; Math. Notes, 114:2 (2023), 199–211
Citation in format AMSBIB
\Bibitem{DurSaf23}
\by D.~K.~Durdiev, J.~Sh.~Safarov, J.~Sh.~Safarov
\paper Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 2
\pages 244--259
\mathnet{http://mi.mathnet.ru/mzm13686}
\crossref{https://doi.org/10.4213/mzm13686}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4665110}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 2
\pages 199--211
\crossref{https://doi.org/10.1134/S0001434623070210}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85168615081}
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  • https://doi.org/10.4213/mzm13686
  • https://www.mathnet.ru/eng/mzm/v114/i2/p244
    • This publication is cited in the following 4 articles:
    1. J. Sh. Safarov, “Inverse Problem for a Non-Homogeneous Integro-Differential Equation of the Hyperbolic Type”, Vestnik St.Petersb. Univ.Math., 57:1 (2024), 97  crossref
    2. D. K. Durdiev, T. R. Suyarov, “Inverse coefficient problem for the 2D wave equation with initial and nonlocal boundary conditions”, Vladikavk. matem. zhurn., 26:2 (2024), 5–25  mathnet  crossref
    3. J. Sh. Safarov, U. N. Kalandarov, M. J. Safarova, “Inverse Problem of Determining a Kernel of the Viscoelasticity Equation with Distributed Data in a Limited Domain”, Lobachevskii J Math, 45:7 (2024), 3380  crossref
    4. Z. A. Sobirov, “Inverse source problem for the subdiffusion equation on a metric star graph with integral overdetermination condition”, Lobachevskii J Math, 44:12 (2023), 5426  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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