Exponential decay for Maxwell equations with a boundary memory condition

We study the asymptotic behavior of the solution of the Maxwell equations with the following boundary condition of memory type: Eτ (t ) = η0H(t )×n+ ∞ 0 η(s)H(t − s) ×n ds. (0.1) We consider a ‘Graffi’ type free energy and we prove that, if the kernel η satisfies the condition η +κη > 0 and the domain Ω is strongly star shaped, then the energy of the solution exponentially decays. We also prove that the exponential decay of η is a necessary condition for the exponential decay of the solution.  2004 Elsevier Inc. All rights reserved.