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 Num. Meth. Prog., 2014, Volume 15, Issue 3, Pages 411–416 (Mi vmp260)

To the inverse heat conduction problem

V. A. Morozova, A. N. Markovskyb, V. G. Lezhnevb

a M.V. Lomonosov Moscow State University, Research Computing Center
b Kuban State University

Abstract: An algorithm for the regularization of the inverse heat conduction problem is proposed on the basis of the Fourier method. Unlike many other algorithms, the proposed algorithm does not increase the order of the differential equation. The correctness of the regularized problem is proved and its solution is estimated. A problem of another type is formulated; this problem consists in the determination of sources such that the solution of the resulting boundary value problem asymptotically satisfies the final distribution. This limit problem can be considered as a natural alternative for the inverse problem.

Keywords: inverse heat conduction problem, ill-posed problems, regularization, heat conduction, projection algorithm, complete systems of potentials.

Full text: PDF file (171 kB)
UDC: 517.958; 519.632.8

Citation: V. A. Morozov, A. N. Markovsky, V. G. Lezhnev, “To the inverse heat conduction problem”, Num. Meth. Prog., 15:3 (2014), 411–416

Citation in format AMSBIB
\Bibitem{MorMarLez14} \by V.~A.~Morozov, A.~N.~Markovsky, V.~G.~Lezhnev \paper To the inverse heat conduction problem \jour Num. Meth. Prog. \yr 2014 \vol 15 \issue 3 \pages 411--416 \mathnet{http://mi.mathnet.ru/vmp260}