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. 
Andrey Fursikov, Lyubov Shatina
math.OC