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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 2, Pages 125–135 (Mi timm702)

On the reconstruction of inputs in linear parabolic equations

V. I. Maksimov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The problem of reconstructing distributed inputs in linear parabolic equations is investigated. The algorithm proposed for solving this problem is stable with respect to information disturbances and computational errors. It is based on the combination of methods from the theory of ill-posed problems and from the theory of positional control. The process of reconstructing unknown inputs implemented by the algorithm employs inaccurate measurements of phase coordinates of the system at discrete sufficiently frequent times. In the case when the input is a function of bounded variation, an upper estimate is established for the convergence rate.

Keywords: dynamic reconstruction, method of controlled models.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 276, suppl. 1, S126–S137

Bibliographic databases:

UDC: 517.2+519.63

Citation: V. I. Maksimov, “On the reconstruction of inputs in linear parabolic equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 125–135; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S126–S137

Citation in format AMSBIB
\Bibitem{Mak11} \by V.~I.~Maksimov \paper On the reconstruction of inputs in linear parabolic equations \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 2 \pages 125--135 \mathnet{http://mi.mathnet.ru/timm702} \elib{https://elibrary.ru/item.asp?id=17870028} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2012 \vol 276 \issue , suppl. 1 \pages S126--S137 \crossref{https://doi.org/10.1134/S0081543812020101} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305482900010} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84859350574} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. L. Grigorenko, “A control problem with dominating uncertainty”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 68–76
2. V. I. Maksimov, “An algorithm for dynamic reconstruction of the right-hand side of a second-order equation with distributed parameters”, Comput. Math. Math. Phys., 57:8 (2017), 1248–1261
3. Ushakov V.N., Malev A.G., “Stability Defect Estimation For Sets in a Game Approach Problem At a Fixed Moment of Time”, Dokl. Math., 100:3 (2019), 533–537
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