A fourth order parabolic equation modeling epitaxial thin film growth
Abstract. We study the continuum model for epitaxial thin film growth from , which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of non-trivial equilibria in terms of the size of the underlying domain.
In an investigation of asymptotical behavior, we give a weak assumption under which the $\omega$-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples.
 Ortiz, M., Repetto, E.A., Si, H.: A continuum model of kinetic roughening and coarsening in thin films, Journal of the Mechanics and Physics of Solids, Vol. 47, 697-730 (1999)