naa a22 4500 510811825 CHVBK 20180411083446.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813020090 doi (NATIONALLICENCE)springer-10.1134/S0081543813020090 Reconstruction of boundary controls in parabolic systems [Elektronische Daten] [A. Korotkii, D. Mikhailova] In the paper, an inverse dynamic problem is considered. It consists in reconstructing a priori unknown boundary controls in dynamical systems described by boundary value problems for partial differential equations of parabolic type. The source information for solving the inverse problem is the results of approximate measurements of the states of the observed system's motion. The problem is solved in the static case; i.e., to solve it, we use all the measurement data accumulated during some specified observation interval. The problem under consideration is ill-posed. To solve it, we propose the Tikhonov method with a stabilizer containing the sum of the mean-square norm and total time variation of the control. The use of such nondifferentiable stabilizer allows us to obtain more precise results than the approximation of the desired control in the Lebesgue spaces. In particular, this method provides the pointwise and piecewise uniform convergences of regularized approximations and makes possible the numerical reconstruction of the subtle structure of the desired control. In the paper, the subgradient projection method for obtaining a minimizing sequence for the Tikhonov functional is described and substantiated. Also, we demonstrate the two-stage finitedimensional approximation of the problem and present the results of numerical simulation. Pleiades Publishing, Ltd., 2013 dynamical system nationallicence control nationallicence reconstruction nationallicence observation nationallicence measurement nationallicence inverse problem nationallicence regularization nationallicence the Tikhonov method nationallicence variation nationallicence piecewise uniform convergence nationallicence Korotkii A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Mikhailova D. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 98-118 0081-5438 280<98 2013 280 11501 https://doi.org/10.1134/S0081543813020090 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813020090 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Korotkii A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 700 1- Mikhailova D. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 98-118 0081-5438 280<98 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer