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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2019, Volume 60, Issue 2, Pages 93–106
DOI: https://doi.org/10.15372/PMTF20190208 (Mi pmtf462) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Inverse problem for an equation with a nonstandard growth condition

S. N. Antontseva, S. E. Aitzhanovb

a Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Al-Farabi Kazakh National University, Almaty, 050038, Kazakhstan
Full-text PDF (283 kB) Citations (2)
DOI: https://doi.org/10.15372/PMTF20190208
Abstract: This paper describes an inverse problem for determining the right side of a parabolic equation with a nonstandard growth condition and integral overdetermination condition. The Galerkin method is used to prove the existence of two solutions of the inverse problem and their uniqueness, one of them being local and the other one being global in time. Sufficient blow-up conditions for the local condition for a finite time in a limited region with a homogeneous Dirichlet condition on its boundary. The blow-up of the solution is proven using the Kaplan method. The asymptotic behavior of the inverse problem solutions for large time values is investigated. Sufficient conditions for vanishing of the solution for a finite time are obtained. Boundary conditions ensuring the corresponding behavior of the solutions are considered.
Keywords: inverse problem, integral overdetermination condition, parabolic equations with a nonstandard growth condition, solvability, blow-up of the solution, asymptotic solution behavior.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.W03.31.0002
Ministry of Education and Science of the Republic of Kazakhstan AP05132041
Received: 22.10.2018
Revised: 22.10.2018
Accepted: 29.10.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2019, Volume 60, Issue 2, Pages 265–277
DOI: https://doi.org/10.1134/S0021894419020081
Bibliographic databases:
Document Type: Article
UDC: 517.956+517.957+517.956.4
Language: Russian
Citation: S. N. Antontsev, S. E. Aitzhanov, “Inverse problem for an equation with a nonstandard growth condition”, Prikl. Mekh. Tekh. Fiz., 60:2 (2019), 93–106; J. Appl. Mech. Tech. Phys., 60:2 (2019), 265–277
Citation in format AMSBIB
\Bibitem{AntAit19}
\by S.~N.~Antontsev, S.~E.~Aitzhanov
\paper Inverse problem for an equation with a nonstandard growth condition
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 2
\pages 93--106
\mathnet{http://mi.mathnet.ru/pmtf462}
\crossref{https://doi.org/10.15372/PMTF20190208}
\elib{https://elibrary.ru/item.asp?id=37248712}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 2
\pages 265--277
\crossref{https://doi.org/10.1134/S0021894419020081}
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  • https://www.mathnet.ru/eng/pmtf/v60/i2/p93
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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