  We consider the modification of the Cahn-Hilliard equation when a time delay
process through a memory function is taken into account. We then study the
process of spinodal decomposition in fast phase transitions associated with a
conserved order parameter. The introduced memory effect plays an important role
to obtain a finite group velocity. Then, we discuss the constraint for the
parameters to satisfy causality. The memory effect is seen to affect the
dynamics of phase transition at short times and has the effect of delaying, in
a significant way, the process of rapid growth of the order parameter that
follows a quench into the spinodal region.
