The influences of dynamic effects on the growth of islets on the surface of thin films is for the first time considered within the framework of continuum mechanics. The film is modeled with a liquid layer with an inertial free surface at which islets arise and grow. Based on this model, it is demonstrated that an increase in the mass growth rate of the islet nucleus (enlargement of the islet on the film surface) is associated with the known phenomenon of localization of waves in continuum media containing inertial inclusions. The mathematical statement of the problem reduces to an analysis of a system of nonlinear equations describing the growth of islet nuclei and wave propagation in thin films.