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Matematicheskie Trudy, 2019, Volume 22, Number 1, Pages 178–204
DOI: https://doi.org/10.33048/mattrudy.2019.22.107 (Mi mt352) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Inverse problems with pointwise overdetermination for some quasilinear parabolic systems

S. G. Pyatkovab, V. V. Rotkoa

a Yugra State University, Khanty-Mansiisk, 628012 Russia
b Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia
Full-text PDF (312 kB) Citations (7)
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DOI: https://doi.org/10.33048/mattrudy.2019.22.107
Abstract: In the article, we examine well-posedness questions in the Sobolev spaces of the inverse source problem in the case of a quasilinear parabolic system of the second order. The main part of the operator is linear. The overdetermination conditions are values of a solution at some collection of interior points. It is demonstrated that, in the case of at most linear growth of the nonlinearity, there exists a unique global (in time) solution and the problem is well-posed in the Sobolev classes. The conditions on the data are minimal and the results are sharp.
Key words: parabolic system, inverse problem, source function, convection-diffusion, heat-and-mass transfer.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00620_а
The work was supported by the Russian Foundation for Basic Research (Project No. 18–01–00620).
Received: 27.07.2018
Revised: 22.09.2018
Accepted: 10.10.2018
English version:
Siberian Advances in Mathematics, 2020, Volume 30, Issue 2, Pages 124–142
DOI: https://doi.org/10.3103/S1055134420020054
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: S. G. Pyatkov, V. V. Rotko, “Inverse problems with pointwise overdetermination for some quasilinear parabolic systems”, Mat. Tr., 22:1 (2019), 178–204; Siberian Adv. Math., 30:2 (2020), 124–142
Citation in format AMSBIB
\Bibitem{PyaRot19}
\by S.~G.~Pyatkov, V.~V.~Rotko
\paper Inverse problems with pointwise overdetermination for some quasilinear parabolic systems
\jour Mat. Tr.
\yr 2019
\vol 22
\issue 1
\pages 178--204
\mathnet{http://mi.mathnet.ru/mt352}
\crossref{https://doi.org/10.33048/mattrudy.2019.22.107}
\transl
\jour Siberian Adv. Math.
\yr 2020
\vol 30
\issue 2
\pages 124--142
\crossref{https://doi.org/10.3103/S1055134420020054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85086272950}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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