NUMERICAL COMPUTATIONS OF COARSENING IN THE ONE-DIMENSIONAL CAHN-HILLIARD MODEL OF PHASE-SEPARATION

Time dependent solutions of the Cahn-Hilliard equation are studied numerically. In particular heteroclinic orbits, which connect different equilibrium solutions at t = -infinity and t = +infinity, are sought. Thus boundary value problems in space-time are computed. This computation requires an investigation of the stability of equilibria, since projections onto the stable and unstable manifolds determine the boundary conditions at t = -infinity and t = +infinity. This stability analysis is then followed by solution of the appropriate boundary value problem in space-time. The results obtained cannot be found by standard initial value simulations. By specifying the two steady states at t = +/-infinity appropriately it is possible to find orbits reflecting a given degree of coarsening over the time evolution. This gives a clear picture of the dynamic coarsening admissible in the equation. It also provides an understanding of orbits on the global attractor for the equation.