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

Journal Article · Tue Jun 30 00:00:00 EDT 2009 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2009V200N05ABEH004014; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21301608

Magaril-Il'yaev, G G ^[1]; Osipenko, Konstantin Yu ^[2]

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1. Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow (Russian Federation)
2. Moscow State Aviation Technological University, Moscow (Russian Federation)

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.

• OSTI ID: 21301608
• Journal Information: Sbornik. Mathematics, Vol. 200, Issue 5; Other Information: DOI: 10.1070/SM2009v200n05ABEH004014; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
EQUATIONS
ERRORS
HEAT
INFORMATION THEORY
MATHEMATICAL SOLUTIONS
TEMPERATURE DISTRIBUTION