Guided waves in a fluid layer on an elastic irregular bottom

In this paper one considers the linearized problem to determine the movement of an ideal heavy fluid contained in an unbounded container with elastic walls. As initial data one knows the movement of both the bottom and the free surface of the fluid and also the strength of certain perturbation, strong enough to take the bottom out of its rest state.

One important point to be considered regards the influence of the bottom's geometry on the propagation of superficial waves. This problem has been already studied in other works without considering the elastic properties of the bottom and considering a cilindrical container with bounded section.