Long-time behavior and energy growth for electromagnetic waves reflected by a moving boundary

The author studies 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 he establishes 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→∞ of the solutions. The 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→∞, irrespective of the initial data