On the decay of the local energy for wave equations with a moving obstacle

Source abstract

Recently the decay of the local energy for wave equations with a moving obstacle has been studied by Cooper [1] and Cooper and Strauss [2] etc. In their works it has been assumed that the obstacle is uniformly bounded in time t and that the origin is contained in for all t > 0 and is star-shaped with respect to the origin. (The second condition has been assumed implicitly in [2] (see Assumption (B), [2]).)