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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1393–1409
DOI: https://doi.org/10.33048/semi.2019.16.097 (Mi semr1138) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differentical equations, dynamical systems and optimal control

Behavior of solutions to an inverse problem for a quasilinear parabolic equation

S. E. Aitzhanovab, D. T. Zhanuzakovaa

a Al-Farabi Kazakh National University 71, Al-Farabi ave., Almaty, 050038, Kazakhstan
b Kazakhstan Institute of Mathematics and Mathematical Modeling 125, Pushkina str., Almaty, 050010, Kazakhstan
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DOI: https://doi.org/10.33048/semi.2019.16.097
Abstract: In this article we consider the inverse problem with an integral condition by redefinition for a parabolic type equation. The existence of a weak solution of the inverse problem is proved by the Galerkin method.In a bounded domain with a homogeneous Dirichlet condition, sufficient conditions for the destruction of its solution in a finite time are obtained, and also the stability of the solution for the inverse problem with the opposite sign on the nonlinearity of the power type.
Keywords: inverse problems, blowing-up solutions, stability, integral overdetermination condition.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP05132041
The work is supported by MES RK (grant AP05132041).
Received March 20, 2019, published October 9, 2019
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35R30,35K55
Language: English
Citation: S. E. Aitzhanov, D. T. Zhanuzakova, “Behavior of solutions to an inverse problem for a quasilinear parabolic equation”, Sib. Èlektron. Mat. Izv., 16 (2019), 1393–1409
Citation in format AMSBIB
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\by S.~E.~Aitzhanov, D.~T.~Zhanuzakova
\paper Behavior of solutions to an inverse problem for a quasilinear parabolic equation
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1393--1409
\mathnet{http://mi.mathnet.ru/semr1138}
\crossref{https://doi.org/10.33048/semi.2019.16.097}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000491070500001}
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