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J. Sib. Fed. Univ. Math. Phys., 2017, Volume 10, Issue 1, Pages 4–15 (Mi jsfu516)  
This article is cited in 2 scientific papers (total in 2 papers)

The inverse problem for the nonlinear pseudoparabolic equation of filtration type

Anna Sh. Lyubanova

Institute of Space and Information Technologies, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: The paper discusses the correctness of the inverse problem on finding an unknown coefficient dependent on $t$ in the nonlinear pseudoparabolic equation of the third order with an additional information on the boundary. The existence and uniqueness theorem is proven. The proof of the theorem is carried out by the reduction of the original inverse problem to the equivalent one with an operator equation for the unknown coefficient.

Keywords: local existence and uniqueness theorem, a priori estimate, inverse problem, nonlinear higher-order equation, pseudoparabolic equation, filtration.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
This research was supported by the Government of the Russian Federation, grant 14.Y26.31.0006.


DOI: https://doi.org/10.17516/1997-1397-2017-10-1-4-15

Full text: PDF file (146 kB)
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Bibliographic databases:

UDC: 517.95
Received: 25.06.2016
Received in revised form: 10.09.2016
Accepted: 20.11.2016
Language:

Citation: Anna Sh. Lyubanova, “The inverse problem for the nonlinear pseudoparabolic equation of filtration type”, J. Sib. Fed. Univ. Math. Phys., 10:1 (2017), 4–15

Citation in format AMSBIB
\Bibitem{Lyu17}
\by Anna~Sh.~Lyubanova
\paper The inverse problem for the nonlinear pseudoparabolic equation of filtration type
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2017
\vol 10
\issue 1
\pages 4--15
\mathnet{http://mi.mathnet.ru/jsfu516}
\crossref{https://doi.org/10.17516/1997-1397-2017-10-1-4-15}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412012600001}


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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. N. Shergin, E. I. Safonov, S. G. Pyatkov, “On some inverse coefficient problems with the pointwise overdetermination for mathematical models of filtration”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:1 (2019), 82–95  mathnet  crossref  elib
    2. A. Sh. Lyubanova, A. V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion”, Appl. Anal., 98:11 (2019), 1997–2010  crossref  mathscinet  zmath  isi  scopus
    		• Журнал Сибирского федерального университета. Серия "Математика и физика"
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