On a~control problem associated with the heat transfer process
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 17-30.

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Mathematical models of thermocontrol processes are considered. In the model under consideration, the temperature inside a domain is controlled by m convectors acting on the boundary. The control parameter is a vector-function, which components are equal to the magnitude of output of hot or cold air producing by each convector. The necessary and sufficient conditions for achieving the given projection of the temperature into some m-dimensional subspace are studied.
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Sh. Alimov. On a~control problem associated with the heat transfer process. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 17-30. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a1/

[1] N. I. Akhiezer, I. M. Glazman, Theory of Linear Operators in Hilbert Space, Nauka, Moscow, 1966 (in Russian) | Zbl

[2] S. Albeverio, Sh. Alimov, “On a time-optimal control problem associated with the heat exchange process”, Applied Mathematics and Optimization, 57:1 (2008), 58–68 | DOI | MR | Zbl

[3] V. Barbu, A. Răşcanu, G. Tessitore, “Carleman estimates and controllability of linear stochastic heat equations”, Applied Mathematics and Optimization, 47:2 (2003), 97–120 | DOI | MR | Zbl

[4] H. O. Fattorini, “Time and norm optimal control for linear parabolic equations: necessary and sufficient conditions”, Control and Estimation of Distributed Parameter Systems, International Series of Numerical Mathematics, 143, Birkhäuser, Basel, 2002, 151–168

[5] A. V. Fursikov, Optimal Control of Distributed Systems. Theory and Applications, Translations of Math. Monographs, 187, Amer. Math. Soc., Providence, Rhode Island, 2000 | MR

[6] P. Gurevich, W. Jäger, A. Skubachevskii, “On periodicity of solutions for thermocontrol problems with hysteresis-type switches”, SIAM J. Math. Anal., 41:2 (2009), 733–752 | DOI | MR | Zbl

[7] T. Kato, Perturbations Theory for Linear Operators, Springer-Verlag, NY, 1966 | MR

[8] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Linear and Quasi-Linear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian) | MR

[9] O. A. Ladyzhenskaya, N. N. Uraltseva, Linear and Quasi-Linear Equations of Elliptic Type, Nauka, Moscow, 1964 (in Russian) | MR

[10] J. L. Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Dunod Gauthier-Villars, Paris, 1968 | MR

[11] A. N. Tikhonov, A. A. Samarsky, Equations of Mathematical Physics, Nauka, Moscow, 1966 (in Russian) | Zbl

[12] V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker, NY, 1971 | MR | Zbl