An Example of Pure Stability for the Wave Equation with Moving Boundary

This paper studies the behavior of the energy of the wave equation solution in a finite moving domain 0-x-a t. with a t. assumed to move slower than light and periodically. Moreover, a is continuous, piecewise linear with two independent parameters. The boundary conditions are of Dirichlet type. We show that the energy is always bounded and give results which involve only the independent parameters. The proof is based on the determination of the invariant measure of a homeomorphism of the circle related to a.