On (exponential) stability for systems with propagation phenomena

It is considered the problem of stabilizing the torsional vibrations of a distributed flexible beam using boundary control. A Lyapunov functional obtained by modifying the energy functional is introduced, thus allowing to obtain exponential stability under quite mildly restrictive conditions. The bounded peaking problem is also discussed within the same framework. The paper ends by pointing other research problems which might be revisited within the aforementioned Lyapunov framework.