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 Mathematical notes of NEFU: Year: Volume: Issue: Page: Find

 Mathematical notes of NEFU, 2016, Volume 23, Issue 4, Pages 31–45 (Mi svfu37)

Mathematics

Inverse problems of recovering the right-hand side of a special type of parabolic equations

A. I. Kozhanovab

a Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk 630090, Russia
b Novosibirsk State University, 2 Pirogov Street, 2, Novosibirsk 630090, Russia

Abstract: We study the solvability of new inverse problems of finding a solution of some parabolic equation along with the unknown external source (the right-hand side) of a special type. The existence and uniqueness theorems for regular solutions are proved. The considered problems can be treated as generalizations known in the theory of parabolic equations inverse problems with final and integral overdetermination.

Keywords: parabolic equation, linear inverse problem, final or integral overdetermination, unknown coefficient of a special type, existence, uniqueness.

 Funding Agency Grant Number Russian Foundation for Basic Research 15-01-06582

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Document Type: Article
UDC: 517.946

Citation: A. I. Kozhanov, “Inverse problems of recovering the right-hand side of a special type of parabolic equations”, Mathematical notes of NEFU, 23:4 (2016), 31–45

Citation in format AMSBIB
\Bibitem{Koz16} \by A.~I.~Kozhanov \paper Inverse problems of recovering the right-hand side of a special type of parabolic equations \jour Mathematical notes of NEFU \yr 2016 \vol 23 \issue 4 \pages 31--45 \mathnet{http://mi.mathnet.ru/svfu37} \elib{http://elibrary.ru/item.asp?id=29959200}