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As a preparation for the dynamical investigations, this paper begins with ashort review of the three-layer gravastar model with distinguished attention tothe structure of the pertinent parameter space of gravastars in equilibrium.Then the radial stability of these types of gravastars is studied bydetermining their response for the totally inelastic collision of their surfacelayer with a dust shell. It is assumed that the dominant energy condition holdsand the speed of sound does not exceed that of the light in the matter of thesurface layer. While in the analytic setup the equation of state is kept to begeneric, in the numerical investigations three functionally distinct classes ofequations of states are applied. In the corresponding particular cases themaximal mass of the dust shell that may fall onto a gravastar withoutconverting it into a black hole is determined. For those configurations whichremain stable the excursion of their radius is assigned. It is found that eventhe most compact gravastars cannot get beyond the lower limit of the size ofconventional stars, provided that the dominant energy condition holds in bothcases. It is also shown---independent of any assumption concerning the matterinterbridging the internal de Sitter and the external Schwarzschildregions---that the better is a gravastar in mimicking a black hole the easieris to get the system formed by a dust shell and the gravastar beyond the eventhorizon of the composite system. In addition, a generic description of thetotally inelastic collision of spherical shells in spherically symmetricspacetimes is also provided in the appendix.

Probing the stability of gravastars by dropping dust shells onto them