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Bilinear control system with the reaction‐diffusion term satisfying Newton's law
Author(s) -
Lin P.,
Leid P.,
Gao H.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510292
Subject(s) - controllability , term (time) , mathematics , heat equation
In this paper, we discuss a parabolic system governed by bilinear control, modeled according to Newton's Law. At first we prove that the system is exactly null controllable in long time T > 0 by locally distributed bilinear control and we further prove the exact null controllability in long time T > 0 of the semilinear parabolic equation y t ‐Δ y + b |∇ y| 2 =ξ o u with traditionally additive locally distributed control and the existence of the control optimal time for the system. Then, we deduce an exact controllability result to particular stationary functions when we are acting over the whole domain and to particular stationary functions vanishing outside some ball included in the control domain when the control domain is as small as we want.