  We study the free-surface deformation dynamics of an immersed glassy thin
polymer film supported on a substrate, induced by an air nanobubble at the free
surface.We combine analytical and numerical treatments of the glassy thin film
equation, resulting from the lubrication approximation applied to the surface
mobile layer of the glassy film, under the driving of an axisymmetric step
function in the pressure term accounting for the nanobubble's Laplace pressure.
Using the method of Green's functions, we derive a general solution for the
film profile. We show that the lateral extent of the surface perturbation
follows an asymptotic viscocapillary power-law behaviour in time, and that the
film's central height decays logarithmically in time in this regime. This
process eventually leads to film rupture and dewetting at finite time, for
which we provide an analytical prediction exhibiting explicitly the
dependencies in surface mobility, film thickness and bubble size, among others.
Finally, using finite-element numerical integration, we discuss how non-linear
effects induced by the curvature and film profile can affect the evolution.
