We study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show existence of global-in-time weak solutions in two space dimensions, assuming periodic boundary conditions. We also establish exponential-in-time a priori estimates on the H 3 norm of solutions. These bounds enable us to prove the uniqueness of weak solutions. We also show the regularizing effect of the equation on the data.
|Original language||English (US)|
|Number of pages||19|
|Journal||SIAM Journal on Mathematical Analysis|
|State||Published - 2012|
- Cahn-Hilliard type equation
- Global weak solution