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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 10 scientific papers (total in 10 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 (10)
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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 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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