Problem of Low-frequency Localized Oscillations in a Thin Film with Growing Islands

Influence of localization waves to islands growing on a thin film is investigated. The film is modelled as a fluid layer covered by an inertial surface with the variable density of mass and surface tension. Mathematically, the problem is reduces to analysis of a system of non-linear equations describing the growth of island nuclei and wave propagation in the films. The existence of trapped modes for the corresponding frequency-domain problem is established. We show that for large time wave localization near islands gives some contribution in the increase of the velocity of island growth.