The main objectives of this article are two-fold. First, we study the effect
of the nonlinear Onsager mobility on the phase transition and on the
well-posedness of the Cahn-Hilliard equation modeling a binary system. It is
shown in particular that the dynamic transition is essentially independent of
the nonlinearity of the Onsager mobility. However, the nonlinearity of the
mobility does cause substantial technical difficulty for the well-posedness and
for carrying out the dynamic transition analysis. For this reason, as a second
objective, we introduce a systematic approach to deal with phase transition
problems modeled by quasilinear partial differential equation, following the
ideas of the dynamic transition theory developed recently by Ma and Wang
