Stabilization of a semilinear parabolic equation in the exterior of a bounded domain by means of boundary controls

The problem of the stabilization of a semilinear equation in the exterior of a bounded domain is considered. In view of the impossibility of an exponential stabilization of the form $e^{-\sigma t}$ of the solution of a parabolic equation in an unbounded domain no matter what the boundary control is, one poses the problem of power-like stabilization by means of a boundary control. For a fixed initial condition and parameter $k>0$ of the rate of stabilization the existence of a boundary control such that the solution approaches zero at the rate $1/t^k$ is demonstrated.