BOUNDARY STABILIZATION OF MAXWELL EQUATIONS

We consider Maxwell's equations with the Silver-Miller absorbing boundary conditions in a bounded domain of R3. Assuming that the domain is star-shaped we prove the exponential energy decay of the solutions. As a consequence, we improve some earlier exact controllability theorems by weakening their time assumptions. Our results are optimal if OMEGA is a ball. The proofs are based on a new identity obtained by the multiplier method.