Abstract:
In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in u in which the coefficients of ut and u depend on u(x,t) , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.
\Bibitem{Tka04}
\by D.~S.~Tkachenko
\paper On an Inverse Problem for a Parabolic Equation
\jour Mat. Zametki
\yr 2004
\vol 75
\issue 5
\pages 729--743
\mathnet{http://mi.mathnet.ru/mzm71}
\crossref{https://doi.org/10.4213/mzm71}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2085736}
\zmath{https://zbmath.org/?q=an:1059.35177}
\elib{https://elibrary.ru/item.asp?id=6618276}
\transl
\jour Math. Notes
\yr 2004
\vol 75
\issue 5
\pages 676--689
\crossref{https://doi.org/10.1023/B:MATN.0000030976.63035.e1}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000222492400010}
Linking options:
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https://doi.org/10.4213/mzm71
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This publication is cited in the following 3 articles:
Dinh Nho Hao Bui Viet Huong Nguyen Thi Ngoc Oanh Phan Xuan Thanh, “Determination of a term in the right-hand side of parabolic equations”, J. Comput. Appl. Math., 309 (2017), 28–43
Erdem A., “An Adaptive Algorithm For Determination of Source Terms in a Linear Parabolic Problem”, J. Inverse Ill-Posed Probl., 22:4 (2014), 569–592
Yaman M., “Blow-Up Solution and Stability to an Inverse Problem for a Pseudo-Parabolic Equation”, J. Inequal. Appl., 2012, 274