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 Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 5, Page 859 (Mi zvmmf10897)

Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition

M. I. Ismailova, S. Erkovanb

a Gebze Technical University, Department of Mathematics, 41400, Gebze/Kocaeli, Turkey
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, AZ1141 Baku, Azerbaijan

Abstract: We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The global well-posedness of the problem is obtained by generalized Fourier method combined with the unique solvability of the second kind Volterra integral equation. For obtaining a numerical solution of the inverse problem, we propose the discretization method from a new combination. On the one hand, it is known the traditional method of uniform finite difference combined with numerical integration on a uniform grid (trapezoidal and Simpson's), on the other hand, we give the method of non-uniform finite difference is combined by a numerical integration on a non-uniform grid (with Gauss–Lobatto nodes). Numerical examples illustrate how to implement the method.

Key words: 2D heat equation, Volterra integral equation, Ionkin-type boundary condition, generalized Fourier method, uniform finite difference method, non-uniform finite difference method, numerical integration.

DOI: https://doi.org/10.1134/S0044466919050168

English version:
Computational Mathematics and Mathematical Physics, 2019, 59:5, 791–808

Bibliographic databases:

Revised: 25.06.2018
Accepted:11.01.2019
Language:

Citation: M. I. Ismailov, S. Erkovan, “Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 859; Comput. Math. Math. Phys., 59:5 (2019), 791–808

Citation in format AMSBIB
\Bibitem{IsmErk19} \by M.~I.~Ismailov, S.~Erkovan \paper Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2019 \vol 59 \issue 5 \pages 859 \mathnet{http://mi.mathnet.ru/zvmmf10897} \crossref{https://doi.org/10.1134/S0044466919050168} \elib{https://elibrary.ru/item.asp?id=37310688} \transl \jour Comput. Math. Math. Phys. \yr 2019 \vol 59 \issue 5 \pages 791--808 \crossref{https://doi.org/10.1134/S0965542519050087} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000472151500010} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067498328} 

• http://mi.mathnet.ru/eng/zvmmf10897
• http://mi.mathnet.ru/eng/zvmmf/v59/i5/p859

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. G. Pyatkov, “O nekotorykh klassakh obratnykh zadach ob opredelenii funktsii istochnikov dlya sistem teplomassoperenosa”, Differentsialnye uravneniya i matematicheskoe modelirovanie, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 23–42