  We propose a model to describe an evolution of a bubble cluster with rupture.
In a special case, the equation is reduced to a single parabolic equation with
evaporation for the thickness of a liquid layer covering bubbles. We postulate
that a bubble collapses if this liquid layer becomes thin. We call this
collapse a rupture. We prove for our model that there is a periodic-in-time
solution if the place of rupture occurs only in the largest bubble. Numerical
tests indicate that there may not exist a periodic solution if such an
assumption is violated.
