  The stochastic partial differential equation analyzed in this work, is
motivated by a simplified mesoscopic physical model for phase separation. It
describes pattern formation due to adsorption and desorption mechanisms
involved in surface processes, in the presence of a stochastic driving force.
This equation is a combination of Cahn-Hilliard and Allen-Cahn type operators
with a multiplicative, white, space-time noise of unbounded diffusion. We apply
Malliavin calculus, in order to investigate the existence of a density for the
stochastic solution $u$. In dimension one, according to the regularity result
in \cite{AKM}, $u$ admits continuous paths a.s. Using this property, and
inspired by a method proposed in \cite{CW1}, we construct a modified
approximating sequence for $u$, which properly treats the new second order
Allen-Cahn operator. Under a localization argument, we prove that the Malliavin
derivative of $u$ exists locally, and that the law of $u$ is absolutely
continuous, establishing thus that a density exists.
