Variational setting of the problem on the oscillations of a fluid in a vessel with an elastic inclusion

Abstract

The problem on the oscillations of an ideal incompressible fluid in a moving rectangular vessel is studied. One wall of the vessel contains an elastic inclusion. The problem involves two free boundaries—the free surface of the fluid and the surface of the elastic inclusion. It is suggested to solve this problem by using a functional whose variation leads to differential equations with nonlinear kinematic and dynamical conditions on the free boundaries.