  We study spinodal decomposition and coarsening when initiated by localized
disturbances in the Cahn-Hilliard equation. Spatio-temporal dynamics are
governed by multi-stage invasion fronts. The first front invades a spinodal
unstable equilibrium and creates a spatially periodic unstable pattern.
Secondary fronts invade this unstable pattern and create a coarser pattern in
the wake. We give linear predictions for speeds and wavenumbers in this process
and show existence of corresponding nonlinear fronts. The existence proof is
based on Conley index theory, a priori estimates, and Galerkin approximations.
We also compare our results and predictions with direct numerical simulations
and report on some interesting bifurcations.
