Problem of the Distributed Control of the Emulsion Vibrations of Weakly Viscous Compressible Liquids

A problem of the distributed control of oscillations of an effective (averaged) medium corresponding to a two-phase medium of slightly viscous liquids is considered. The averaged model is described by a boundary value problem for an integrodifferential equation. It is shown that for this model, it is impossible to bring the vibrations to a state of rest in finite time by applying force on the entire region.