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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 6, Pages 753–763 (Mi jsfu724)  

Global solvability of the one-dimensional inverse problem for the integro-differential equation of acoustics

Jurabek Sh. Safarovab

a Institute of Mathematics, Uzbekistan Academy of Sciences, Mirzo Ulugbek, 81, Tashkent, 100170
b Tashkent University of Information Technologies, Amir Timur, 108, Tashkent, 100020, Uzbekistan

Abstract: The hyperbolic integro–differential acoustic equation is considered. Direct problem is to find the acoustic pressure from the initial - boundary value problem for this equation with point source located on the boundary of the space domain. The inverse problem is studied. It consists in determining the one-dimensional kernel of the integral term using the solution of the direct problem at $ x = 0$, $ t > 0 $. Inverse problem is reduced to the system of integral equations for unknown functions. The principle of contraction mappings is applied to this system in the space of continuous functions with weighted norms. The global unique solvability of the inverse problem is proved.

Keywords: integrodifferential equation, inverse problem, Dirac delta function, kernel, weight function.

DOI: https://doi.org/10.17516/1997-1397-2018-11-6-753-763

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Bibliographic databases:

UDC: 517.958
Received: 28.01.2018
Received in revised form: 17.10.2018
Accepted: 27.11.2018
Language:

Citation: Jurabek Sh. Safarov, “Global solvability of the one-dimensional inverse problem for the integro-differential equation of acoustics”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 753–763

Citation in format AMSBIB
\Bibitem{Saf18}
\by Jurabek~Sh.~Safarov
\paper Global solvability of the one-dimensional inverse problem for the integro-differential equation of acoustics
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 6
\pages 753--763
\mathnet{http://mi.mathnet.ru/jsfu724}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-6-753-763}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000452216700011}


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