Reachable states for the distributed control of the heat equation

Abstract

We are concerned with the determination of the reachable states for the distributed control of the heat equation on an interval. We consider either periodic boundary conditions or homogeneous Dirichlet boundary conditions. We prove that for a $L^2$ distributed control, the reachable states are in the Sobolev space $H^1$ and that they have complex analytic extensions on squares whose horizontal diagonals are regions where no control is applied.