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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, Volume 33, Issue 1, Pages 90–102
DOI: https://doi.org/10.35634/vm230106
(Mi vuu837)
 

This article is cited in 1 scientific paper (total in 2 paper)

MATHEMATICS

Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition

D. K. Durdieva, J. J. Jumayeva, D. D. Atoevb

a Bukhara Branch of the Institute of Mathematics named after V. I. Romanovskiy at the Academy of Sciences of the Republic of Uzbekistan, ul. M. Ikbal, 11, Bukhara, 200118, Uzbekistan
b Bukhara State University, ul. M. Ikbal, 11, Bukhara, 200118, Uzbekistan
Full-text PDF (154 kB) Citations (2)
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Abstract: In this paper, an inverse problem for a one-dimensional integro-differential heat equation is investigated with nonlocal initial-boundary and integral overdetermination conditions. We use the Fourier method and the Schauder principle to investigate the solvability of the direct problem. Further, the problem is reduced to an equivalent closed system of integral equations with respect to unknown functions. Existence and uniqueness of the solution of the integral equations are proved using a contractive mapping. Finally, using the equivalency, the existence and uniqueness of the classical solution is obtained.
Keywords: integro-differential equation, nonlocal initial-boundary problem, inverse problem, integral equation, Schauder principle.
Received: 20.11.2022
Accepted: 18.01.2023
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35K60, 35R30, 45G15
Language: English
Citation: D. K. Durdiev, J. J. Jumayev, D. D. Atoev, “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 90–102
Citation in format AMSBIB
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\by D.~K.~Durdiev, J.~J.~Jumayev, D.~D.~Atoev
\paper Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2023
\vol 33
\issue 1
\pages 90--102
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\crossref{https://doi.org/10.35634/vm230106}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573570}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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