2017/05/31 by Scholtes, Sebastian, Westdickenberg, Maria G.
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1705.10985
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in H-1 away from a point on the so-called slow manifold with N well-separated layers. Specifically, we show that, for such initial data on a system of lengthscale Λ, there are three phases of evolution: (1) the solution is drawn after a time of order Λ2 into an algebraically small neighborhood of the N-layer branch of the slow manifold, (2) the solution is drawn after a time of order Λ3 into an exponentially small neighborhood of the N-layer branch of the slow manifold, (3) the solution is trapped for an exponentially long time exponentially close to the N-layer branch of the slow manifold. The timescale in phase (3) is obtained with the sharp constant in the exponential.