Doubly nonlocal Cahn-Hilliard equations

We consider a doubly nonlocal nonlinear parabolic equation
which describes phase-segregation of a two-component material in a
bounded domain. This model is a more general version than the recent
nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz,
such that it reduces to the latter under certain conditions. It turns
out that there are four possible cases of double interaction in which
the nonlocality is reflected, we shall discuss some of them.