Stabilization of Linear Parabolic Equations Defined in an Exterior of a Bounded Domain by a Boundary Control

In this paper, we study the stabilization problem for linear parabolic equation defined in an exterior of a bounded domain. For any positive k > 0 and for a given initial datum we prove the existence of a boundary condition which is the control such, that the solution of this boundary-value problem tends to 0 as t with the rate 1/t ^k .