  As a preparation for the dynamical investigations, this paper begins with a
short review of the three-layer gravastar model with distinguished attention to
the structure of the pertinent parameter space of gravastars in equilibrium.
Then the radial stability of these types of gravastars is studied by
determining their response for the totally inelastic collision of their surface
layer with a dust shell. It is assumed that the dominant energy condition holds
and the speed of sound does not exceed that of the light in the matter of the
surface layer. While in the analytic setup the equation of state is kept to be
generic, in the numerical investigations three functionally distinct classes of
equations of states are applied. In the corresponding particular cases the
maximal mass of the dust shell that may fall onto a gravastar without
converting it into a black hole is determined. For those configurations which
remain stable the excursion of their radius is assigned. It is found that even
the most compact gravastars cannot get beyond the lower limit of the size of
conventional stars, provided that the dominant energy condition holds in both
cases. It is also shown---independent of any assumption concerning the matter
interbridging the internal de Sitter and the external Schwarzschild
regions---that the better is a gravastar in mimicking a black hole the easier
is to get the system formed by a dust shell and the gravastar beyond the event
horizon of the composite system. In addition, a generic description of the
totally inelastic collision of spherical shells in spherically symmetric
spacetimes is also provided in the appendix.
