Abstract
This paper deals with controllability for the distributed-parameter systems described by linear partial differential equations of parabolic type in [0, ∞)×Ω, where Ω is a bounded domain in Rn. The purpose of this paper is to improve the result of Sakawa [10] who obtained the necessary and sufficient conditions for the controllability in L2(Ω); we consider the controllability in H1(Ω), the Sobolev space of order 1, and its subspaces. We consider both finite dimensional distributed control appearing in the differential equation and boundary control appearing in the boundary condition. In each control, the condition for the controllability is obtained. Especially, in the case of n=1, the result here is applied to the controllability in the sense of uniform convergence with respect to the space variable. Such conditions guarantee a more precise control input.
