Slow dynamics for the hyperbolic Cahn-Hilliard equation in one-space dimension
The aim of this paper is to study the metastable properties of the solutions to a hyperbolic relaxation of the classic Cahn-Hilliard equation in one-space dimension, subject to either Neumann or Dirichlet boundary conditions. To perform this goal, we make use of an “energy approach," already proposed for various evolution PDEs, including the Allen-Cahn and the Cahn-Hilliard equations. In particular, we shall prove that certain solutions maintain a N-transition layer structure for a very long time, thus proving their metastable dynamics.