Finite-time control for the bilinear heat equation

Abstract

Abstract In this paper, we deal with the multidimensional heat equation governed by a bilinear control. We first investigate the finite-time stability and null controllability properties. Then, we study the global and partial approximate controllability. These results are further applied to establish the exact controllability of the system at hand. Nonnegative controllability results are also discussed. The approaches are based on linear semigroup theory and the controllability of the heat equation with additive controls. An other essential tool that we use here is the classical maximum principle.