In this talk we present work in progress on dynamic metastability for the one-dimensional Cahn-Hilliard equation on the torus.
For initial data which is order one away from the so-called slow manifold N, we identify three phases of evolution:
(1) the solution is attracted at an algebraic in time rate to an algebraically small neighbourhood of N,
(2) the solution is attracted at an exponential in time rate to an exponentially small neighbourhood of N,
(3) the solution is trapped for an exponentially long time exponentially close to N.
Contrary to previous results, we do not need to assume well prepared initial data.
To achieve this, we use a cautious interplay between a general relaxation and a general metastability framework by Otto and Westdickenberg.