2010, Korzec, Maciek Dominik, Nayar, Piotr, Rybka, Piotr

In this paper we study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show global in time existence of weak solutions and uniform in time a priori estimates in the H^3 norm. These bounds enable us to show the uniqueness of weak solutions.

2010, Korzec, Maciek Dominik, Rybka, Piotr

A convective Cahn-Hilliard type equation of sixth order that describes the faceting of a growing surface is considered with periodic boundary conditions. By using a Galerkin approach the existence of weak solutions to this sixth order partial differential equation is established in $L^2(0,T; dot H^3_per)$. Furthermore stronger regularity results have been derived and these are used to prove uniqueness of the solutions. Additionally a numerical study shows that solutions behave similarly as for the better known convective Cahn-Hilliard equation. The transition from coarsening to roughening is analyzed, indicating that the characteristic length scale decreases logarithmically with increasing deposition rate