Appl Math Optim 45:99–123 (2002)
2002 Springer-Verlag New York Inc.
Exact Boundary Controllability of
Electromagnetic Fields in a General Region
M. M. Eller
and J. E. Masters
Department of Mathematics, Georgetown University,
Washington, DC 20057, USA
Cycorp, Inc., 3721 Executive Center Dr. #100,
Austin, TX 78731-1615, USA
Communicated by I. Lasiecka
Abstract. We prove exact controllability for Maxwell’s system with variable co-
efﬁcients in a bounded domain by a current ﬂux in the boundary. The proof relies on
a duality argument which reduces the proof of exact controllability to the proof of
continuous observabilityfor the homogeneous adjoint system. There is no geometric
restriction imposed on the domain.
Key Words. Maxwell’s system, Exact boundary controllability, Continuous
AMS Classiﬁcation. Primary 35, Secondary 49.
1. Introduction and Main Result
Let ⊂ R
be a bounded domain with a C
boundary. We denote the space variable by
x = (x
) and the time variable by t. The electric displacement and the magnetic
induction are denoted by D(t, x) and B(t, x), respectively. Note that these two functions
are vector-valued functions with three components each. The electric permeability is
λ(x) and the magnetic permittivity is κ(x). Throughout this paper we assume these two
functions to be scalar, positive, independent of time and λ, κ ∈ C
(). Moreover, we
assume that the electric conductivity vanishes in and that there are no electric charges
The research of M.E. was supported by the National Science Foundation through Grant DMS-0049020.