Geodesic
Optimal recovery of the solution of the heat equation from inaccurate data
Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 665-682

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The problem of optimal recovery of the solution of the heat equation in the entire space at a fixed instant of time from inaccurate observations of this solution at some other instants of time is investigated. Explicit expressions for an optimal recovery method and its error are given. The solution of a similar problem with a priori information about the temperature distribution at some instants of time is also given. In all cases the optimal method uses information about at most two observations. Bibliography: 22 titles.
Keywords: optimal recovery, convex problem
Mots-clés : Fourier transform. 
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     title = {Optimal recovery of the solution of the heat equation from inaccurate data},
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G. G. Magaril-Il'yaev; K. Yu. Osipenko. Optimal recovery of the solution of the heat equation from inaccurate data. Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 665-682. http://geodesic.mathdoc.fr/item/SM_2009_200_5_a2/