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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 1, Pages 117–127 (Mi jsfu897)

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

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.

DOI: https://doi.org/10.17516/1997-1397-2021-14-1-117-127

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UDC: 517.9
Accepted: 20.10.2020
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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
\Bibitem{DurNur21} \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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000615268200013}