Title :
On the stochastic Cahn-Hilliard equation with reflexions.

Abstract : We present some results on the stochastic Cahn-Hilliard
equation. This is a fourth order equation which appears in many applications.
It describes phase separation in a binary alloy for instance in the presence
of thermal fluctuations. It also describes the motion of random interfaces.
It may contain reflexion terms if one looks only for positive solutions or if
the solution represents a concentration so that it has to be between 0 and 1.
The reflexion is represented  by a reflexion measure in the equation.
We present theoretical results stating existence and uniqueness of solutions.
The main difficulty here is that no comparison principle holds for fourth
order equations. (This is the basic tool in the case of a second order equation).
We also prove that unless a very singular nonlinear term is considered the
reflexion measure does not vanish.
The particular case of a logarithmic nonlinearity is the original model proposed
by Cahn and Hilliard. We show that the standard approximation of the logarithm
by a polynomial is justified.
We also present some numerical simulations.