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: (0.1)Eτ(t)=η0H(t)×n+∫0∞η(s)H(t−s)×nds. 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.