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Journal of Siberian Federal University. Mathematics & Physics, 2021, Volume 14, Issue 1, Pages 117–127
DOI: https://doi.org/10.17516/1997-1397-2021-14-1-117-127
(Mi jsfu897)
 

This article is cited in 6 scientific papers (total in 6 papers)

Determination of a multidimensional kernel in some parabolic integro–differential equation

Durdimurod K. Durdieva, Zhavlon Z. Nuriddinovb

a Bukhara Branch of the Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Bukhara, Uzbekistan
b Bukhara State University, Bukhara, Uzbekistan
Full-text PDF (130 kB) Citations (6)
References:
Abstract: A multidimensional parabolic integro-differential equation with the time-convolution integral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. The inverse problem is studied in this paper. The problem consists in finding the time and spatial dependent kernel of the equation from the solution of direct problem in a hyperplane $x_n=0$ for $t>0 $. This problem is reduced to the more convenient inverse problem with the use of the resolvent kernel. The last problem is replaced by the equivalent system of integral equations with respect to unknown functions. The unique solvability of the direct and inverse problems is proved with use of the principle of contraction mapping.
Keywords: integro-differential equation, inverse problem, Hölder space, kernel, resolvent.
Received: 10.08.2020
Received in revised form: 29.09.2020
Accepted: 20.10.2020
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: Durdimurod K. Durdiev, Zhavlon Z. Nuriddinov, “Determination of a multidimensional kernel in some parabolic integro–differential equation”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 117–127
Citation in format AMSBIB
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\by Durdimurod~K.~Durdiev, Zhavlon~Z.~Nuriddinov
\paper Determination of a multidimensional kernel in some parabolic integro--differential equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 1
\pages 117--127
\mathnet{http://mi.mathnet.ru/jsfu897}
\crossref{https://doi.org/10.17516/1997-1397-2021-14-1-117-127}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000615268200013}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал Сибирского федерального университета. Серия "Математика и физика"
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    References:23
     
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