Problem on Small Motions of a System of Bodies Filled with Ideal Fluids under the Action of an Elastic Damping Device

In this paper, we investigate a problem on small motions of a system of bodies partially filled with ideal fluids under the action of an elastic damping device. The initial boundary value problem is reduced to the Cauchy problem for a first-order differential operator equation on a Hilbert space. Properties of the resulting operator matrices, which are coefficients of the equation, are studied. Theorems on solvability of the Cauchy problem and the initial boundary value problem are proven.