  P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid
spinodal decomposition in non-equilibrium phase separation processes. This
equation contains an inertial term which causes the loss of any regularizing
effect on the solutions. Here we consider an initial and boundary value problem
for this equation in a two-dimensional bounded domain. We prove a number of
results related to well-posedness and large time behavior of solutions. In
particular, we analyze the existence of bounded absorbing sets in two different
phase spaces and, correspondingly, we establish the existence of the global
attractor. We also demonstrate the existence of an exponential attractor.
