On the nonlocal stabilization by starting control of the normal equation generated from the Helmholtz system |
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Authors: | Andrey Fursikov Lyubov Osipova |
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Affiliation: | 1.Department of Mechanics & Mathematics,Moscow State University,Moscow,Russia;2.Mathematical Fluid Dynamics Laboratory,Voronezh State University,Voronezh,Russia |
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Abstract: | We consider the problem of stabilization near zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum. This problem was previously studied in Fursikov and Shatina (2018). As it was recently revealed, the control function suggested in that work contains a term impeding transferring the stabilization construction on the 3D Helmholtz system. The main concern of this paper is to prove that this term is not necessary for the stabilization result, and therefore the control function can be changed by a proper way. |
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