Phase separation of the slightly viscous Cahn-Hilliard equation in the singular perturbation limit

We prove the existence of cluster points in L-1 as epsilon --> 0, say (u) o ver bar, of solutions {u(epsilon)} to a Cahn-Hilliard equation on a domain Q(T) = Omega x (0, T), Omega subset of IRN, with O(epsilon) viscous damping and finite energy initial data. The function ii is then in BV(Q(T)) and ha s values in {-1, +1} for almost all x, t is an element of Q(T). Furthermore the two separated phases Q(+)(t) = {x is an element of Omega : (u) over ba r(x, t) = +1} and Q_(t) = {x is an element of Omega : (u) over bar(x, t) = -1} are well defined and the perimeter of the interface partial derivative Q(+)(t) boolean AND partial derivative Q(-)(t) is bounded. We examine also the limit behavior as t --> infinity of the separated phases.