Problem on oscillation of a body partially filled with an ideal fluid under the action of an elastic and damping forces
We investigate a problem on small motions of a body partially filled with an ideal fluid under the action of an elastic and damping forces. The initial boundary value problem is reduced to the Cauchy problem for a first-order differential operator equation in a Hilbert space. Properties of the resulting operator matrices, which are coefficients of the equation, are studied. Theorems on strong solvability of the Cauchy problem and the initial boundary value problem are proven.