Boundary Controllability of Maxwell's Equations in a Spherical Region

摘要

This paper examines the question of control of electromagnetic fields in a three dimensional spherical region by means of control currents on the boundary of that region. Results of this type are significant in connection with the theory of waveguides, electromagnetic pulse devices, and stealth technology, as well as being of independent mathematical interest. The necessary theory of divergence-free solutions of the vector wave equation is developed. By use of eigenfunctions of the vector Laplacian in appropriate divergence-free domains and moment problem techniques, sufficient conditions for controllability are set forth.