The Dirichlet–Neumann Boundary Control Problem Associated with Maxwell’s Equations in a Cylindrical Region

Abstract

In a cylindrical region we consider electromagnetic fields independent of the axial coordinate: controlling the time evolution of such fields by means of boundary currents, likewise independent of the axial direction, is equivalent to controlling, simultaneously, two wave equations; one with boundary control of Dirichlet type, the other of Neumann type. In this paper we provide a preliminary study of control problems of this type and indicate what is necessary for extensions of our work.