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Mathematical notes of NEFU, 2016, Volume 23, Issue 4, Pages 46–57 (Mi svfu38)  
Mathematics

Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account

S. G. Pyatkovab, V. V. Rotkoa

a Yugra State University, 16 Chekhov Street, Khanty-Mansyisk 628012, Russia
b Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia
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Abstract: We examine the question of well-posedness in the Sobolev spaces of an inverse problem of determining a source function in a system comprising a parabolic equation and an ordinary differential equation. The overdetermination conditions are the values of concentration of an admixture at separate points. We prove existence and uniqueness of solutions to the problem.
Keywords: parabolic equation, inverse problem, heat-and-mass transfer, boundary value problem, source function.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-00063
Received: 20.09.2016
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: S. G. Pyatkov, V. V. Rotko, “Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account”, Mathematical notes of NEFU, 23:4 (2016), 46–57
Citation in format AMSBIB
\Bibitem{PyaRot16}
\by S.~G.~Pyatkov, V.~V.~Rotko
\paper Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account
\jour Mathematical notes of NEFU
\yr 2016
\vol 23
\issue 4
\pages 46--57
\mathnet{http://mi.mathnet.ru/svfu38}
\elib{https://elibrary.ru/item.asp?id=29959201}
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