Andrey Fursikov | Searcharxiv

arXiv2018

On the nonlocal stabilization by starting control of the normal equation generated from Helmholtz system

We consider the problem of stabilization to 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 \cite{FSh16}. As it was recently revealed, the control function suggested in that work contains a term impeding transference the stabilization construction on the 3D Helmholtz system. The main concern of this article 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.

math.OC↗

arXiv2017

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

We consider the semilinear parabolic equation of normal type connected with the 3D Helmholtz equation with periodic boundary condition. The problem of stabilization to zero of the solution for normal parabolic equation with arbitrary initial condition by starting control is studied. This problem is reduced to establishing three inequalities connected with starting control, one of which has been proved previously. The proof for the other two is given here.

math.OC↗