  We consider a finite-size spherical bubble with a nonequilibrium value of the
$q$-field, where the bubble is immersed in an infinite vacuum with the constant
equilibrium value $q_{0}$ for the $q$-field (this $q_{0}$ has already cancelled
an initial cosmological constant). Numerical results are presented for the time
evolution of such a $q$-bubble with gravity turned off and with gravity turned
on. For small enough bubbles and a $q$-field energy scale sufficiently below
the gravitational energy scale $E_\text{Planck}$, the vacuum energy of the
$q$-bubble is found to disperse completely. For large enough bubbles and a
finite value of $E_\text{Planck}$, the vacuum energy of the $q$-bubble
disperses only partially and there occurs gravitational collapse near the
bubble center.
