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Sib. Èlektron. Mat. Izv., 2020, Volume 17, Pages 1106–1127 (Mi semr1278)  

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

Differentical equations, dynamical systems and optimal control

Inverse problem for a second-order hyperbolic integro-differential equation with variable coefficients for lower derivatives

D. K. Durdievab, Zh. D. Totievacd

a Bukhara State University, 11, Mukhammad Iqbol str., Bukhara, 200177, Uzbekistan
b Bukhara Department of the Mathematics Institute, Uzbekistan Academy of Sciences, Bukhara, 200177, Uzbekistan
c Southern Mathematical Institute of Vladikavkaz Scientific Centre, Russian Academy of Sciences, 93a, Markova str., Vladikavkaz, 362002, Russia
d North Ossetian State University, 46, Vatutina str., Vladikavkaz, 362025, Russia

Abstract: The problem of determining the memory of a medium from a second-order equation of hyperbolic type with a constant principal part and variable coefficients for lower derivatives is considered. The method is based on the reduction of the problem to a non-linear system of Volterra equations of the second kind and uses the fundamental solution constructed by S. L. Sobolev for hyperbolic equation with variable coefficients. The theorem of global uniqueness, stability and the local theorem of existence are proved.

Keywords: inverse problem, hyperbolic integro-differential equation, Volterra integral equation, stability, delta function, kernel.

DOI: https://doi.org/10.33048/semi.2020.17.084

Full text: PDF file (387 kB)
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Bibliographic databases:

UDC: 517.958
MSC: 35L20, 35R30, 35Q99
Received February 9, 2020, published August 18, 2020
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Citation: D. K. Durdiev, Zh. D. Totieva, “Inverse problem for a second-order hyperbolic integro-differential equation with variable coefficients for lower derivatives”, Sib. Èlektron. Mat. Izv., 17 (2020), 1106–1127

Citation in format AMSBIB
\Bibitem{DurTot20}
\by D.~K.~Durdiev, Zh.~D.~Totieva
\paper Inverse problem for a second-order hyperbolic integro-differential equation with variable coefficients for lower derivatives
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1106--1127
\mathnet{http://mi.mathnet.ru/semr1278}
\crossref{https://doi.org/10.33048/semi.2020.17.084}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000561108800001}


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    This publication is cited in the following articles:
    1. Durdiev D.K., Zhumaev Zh.Zh., “Memory Kernel Reconstruction Problems in the Integro-Differential Equation of Rigid Heat Conductor”, Math. Meth. Appl. Sci.  crossref  mathscinet  isi  scopus
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