LONG-TIME BEHAVIOR AND ENERGY GROWTH FOR ELECTROMAGNETIC-WAVES REFLECTED BY A MOVING BOUNDARY

We study the phenomenon of a wave reflected back and forth between two parallel, perfectly conducting plates, one of which is oscillating normally to itself. By making a careful analysis of the reflected space-time characteristics we establish a representation formula for the solutions of Maxwell's equations in terms of the initial data. This representation formula together with properties of iterated maps of an interval yield a precise asymptotic description as t --> infinity of the solutions. Our main result is that if there is a finite number of reflected characteristics which are periodic, then the energy of all solutions grows without bound as t --> infinity, irrespective of the initial data.