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Mat. Sb., 2009, Volume 200, Number 5, Pages 37–54 (Mi msb7301)  

This article is cited in 8 scientific papers (total in 8 papers)

Optimal recovery of the solution of the heat equation from inaccurate data

G. G. Magaril-Il'yaeva, K. Yu. Osipenkob

a Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
b Moscow State Aviation Technological University

Abstract: 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, Fourier transform.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7301

Full text: PDF file (594 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:5, 665–682

Bibliographic databases:

UDC: 517.518.8
MSC: Primary 41A65; Secondary 35K05, 46E20, 46E35
Received: 21.09.2008

Citation: G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Mat. Sb., 200:5 (2009), 37–54; Sb. Math., 200:5 (2009), 665–682

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Osipenko K.Yu., “Extremal problems for the generalized heat equation and optimal recovery of its solution from inaccurate data”, Optimization, 60:6 (2011), 755–767  crossref  mathscinet  zmath  isi  elib  scopus
    3. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On Optimal Recovery of Solutions to Difference Equations from Inaccurate Data”, J. Math. Sci., 189:4 (2013), 596–603  crossref  mathscinet  zmath  scopus
    4. N. Temirgaliev, K. E. Sherniyazov, M. E. Berikhanova, “Exact Orders of Computational (Numerical) Diameters in Problems of Reconstructing Functions and Sampling Solutions of the Klein–Gordon Equation from Fourier Coefficients”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S165–S191  mathnet  crossref  crossref  isi  elib
    5. Zhang Y., Lukyanenko D.V., Yagola A.G., “An Optimal Regularization Method For Convolution Equations on the Sourcewise Represented Set”, J. Inverse Ill-Posed Probl., 23:5 (2015), 465–475  crossref  mathscinet  zmath  isi  elib  scopus
    6. Babenko V., Babenko Yu., Parfinovych N., Skorokhodov D., “Optimal recovery of integral operators and its applications”, J. Complex., 35 (2016), 102–123  crossref  mathscinet  zmath  isi  scopus
    7. A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Siberian Math. J., 59:1 (2018), 11–21  mathnet  crossref  crossref  isi  elib
    8. G. G. Magaril-Il'yaev, E. O. Sivkova, “Optimal recovery of semi-group operators from inaccurate data”, Eurasian Math. J., 10:4 (2019), 75–84  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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