16 Pages

Sufficient Conditions for Dirichlet Boundary Control Problems of Parabolic Type

WithFausto Gozzi, Maria Elisabetta Tessitore

This paper is devoted to the search for sufficient optimality conditions for a finite horizon optimal control problem with Dirichlet boundary control and with a semilinear state equation. We prove sufficient conditions for optimality of trajectorycontrol pairs showing a uniqueness result for a system of differential equations which is the Hamiltonian formulation of the classical necessary condition known as the Pontryagin Maximum Principle. This yields a sufficient condition for optimality that extends the results derived in [19] since the state equation is assumed to be linear in order to prove sufficient optimality conditions.