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 Eurasian Math. J., 2011, Volume 2, Number 3, Pages 5–19 (Mi emj59)

On the null-controllability of the heat exchange process

Sh. Alimov

Tashkent Branch of M. V. Lomonosov Moscow State University, Tashkent, Uzbekistan

Abstract: A mathematical model of the heat exchange process, where the temperature inside some domain is controlled by $m$ convectors acting on the boundary, is considered. The control parameter is a vector-function, whose components are equal to the magnitude of the output of hot or cold air produced by each convector. The necessary and sufficient conditions, which initial temperature must satisfy for achieving the zero value by the projection of the temperature into some $m$-dimensional subspace, are studied.

Keywords and phrases: parabolic type operators, heat conduction equation, control of distributed systems.

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MSC: 93C20, 35K05, 35K20
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Citation: Sh. Alimov, “On the null-controllability of the heat exchange process”, Eurasian Math. J., 2:3 (2011), 5–19

Citation in format AMSBIB
\Bibitem{Ali11} \by Sh.~Alimov \paper On the null-controllability of the heat exchange process \jour Eurasian Math. J. \yr 2011 \vol 2 \issue 3 \pages 5--19 \mathnet{http://mi.mathnet.ru/emj59} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2910838} \zmath{https://zbmath.org/?q=an:1253.93010} 

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This publication is cited in the following articles:
1. Tukhtasinov M., Ibragimov G.I., Mamadaliev N.O., “On an Invariant Set in the Heat Conductivity Problem with Time Lag”, Abstract Appl. Anal., 2013, 108482
2. Ergashevich F.Yu., “On the Control of Heat Conduction”, IIUM Eng. J., 19:1 (2018), 168–177
3. Tukhtasinov M., Mustapokulov K., Ibragimov G., “Invariant Constant Multi-Valued Mapping For the Heat Conductivity Problem”, Malays. J. Math. Sci., 13:1 (2019), 61–74
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