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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Acknowledgements
The first author was supported by the Ministry of Education and Science of the Russian Federation (Grant No. 14.Z50.31.0037). The second author was supported by the Russian Foundation for Basic Research (Grant Nos. 15-01-03576 and 15-01-08023).
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Fursikov, A., Osipova, L. On the nonlocal stabilization by starting control of the normal equation generated from the Helmholtz system. Sci. China Math. 61, 2017–2032 (2018). https://doi.org/10.1007/s11425-018-9353-5
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DOI: https://doi.org/10.1007/s11425-018-9353-5