Exponential decay of solutions of Maxwell’s equations coupled with a first-order ordinary differential equation for the polarization

This paper is concerned with Maxwell’s equations involving a first-order ordinary differential equation for the dielectric polarization. The main goal is the exponential convergence of the electromagnetic field to an asymptotic state which is determined by the initial data. This is achieved by the construction of a suitable energy functional involving a vector potential which provides an additional dissipative term for the magnetic field.  2003 Elsevier Inc. All rights reserved