THE VISCOUS CAHN-HILLIARD EQUATION .1. COMPUTATIONS

The viscous Cahn-Hilliard equation arises as a singular limit of the p hase-held model of phase transitions. It contains both the Cahn-Hillia rd and Allen-Cahn equations as particular limits. The equation is in g radient form and possesses a compact global attractor A, comprising he teroclinic orbits between equilibria. Two classes of computation are d escribed. First heteroclinic orbits on the global attractor are comput ed; by using the viscous Cahn-Hilliard equation to perform a homotopy, these results show that the orbits, and hence the geometry of the att ractors, are remarkably insensitive to whether the Allen-Cahn or Cahn- Hilliard equation is studied. Second, initial-value computations are d escribed; these computations emphasize three differing mechanisms by w hich interfaces in the equation propagate for the case of very small p enalization of interfacial energy. Furthermore, convergence to an appr opriate free boundary problem is demonstrated numerically.