# American Institute of Mathematical Sciences

March  2018, 38(3): 1187-1242. doi: 10.3934/dcds.2018050

## Nonlocal stabilization by starting control of the normal equation generated by Helmholtz system

 1 Department of Mechanics & Mathematics, Moscow State University, Moscow 119991, Russia, Voronezh State University, Voronezh, Russia 2 Department of Mechanics & Mathematics, Moscow State University, Moscow 119991, Russia

Received  February 2017 Revised  October 2017 Published  December 2017

Fund Project: The research of the first author was supported by the Ministry of Education and Science of the Russian Federation (grant 14.Z50.31.0037). The second author was supported by RFBR grants 15-01-03576 and 15-01-08023.

Let $y(t,x;y_0)$ be a solution to the semilinear parabolic equation of normal type generated by the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum $y_0(x)$. The problem of stabilization to zero of the solution $y(t,x;y_0)$ by starting control is studied. This problem is reduced to establishing three inequalities connected with starting control, one of which has been proved in [10], [15]. The proof for the other two is given here.

Citation: Andrei Fursikov, Lyubov Shatina. Nonlocal stabilization by starting control of the normal equation generated by Helmholtz system. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1187-1242. doi: 10.3934/dcds.2018050
##### References:

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##### References:
Signs of $c(m)d(l)c(m+l)$
Signs of $c(m)c(l)d(m+l)$
Signs of $A(k)A(k+l)B(l)$
Signs of $(-A(k)A(l)B(k+l))$
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