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Optimal Recovery of Pipe Temperature from Inaccurate Measurements G. G. Magaril-Il'yaev abc ,
K. Yu. Osipenko adb ,
E. O. Sivkova efc a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia b Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia c Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, ul. Vatutina 53, Vladikavkaz, 362027 Russia d Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia e Moscow Pedagogical State University, Malaya Pirogovskaya ul. 1/1, Moscow, 119991 Russia f National Research University Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000 Russia Abstract:
The problem of optimal recovery of the solution of the heat equation on a manifold at a given instant of time from inaccurate measurements of this solution at other instants of time is considered, the manifold being the product of the real line and a circle. A family of optimal recovery methods is constructed.
UDC:
517.984.64 Received: May 25, 2020 Revised: August 18, 2020 Accepted: August 24, 2020
DOI:
10.4213/tm4139
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