# A fourth order parabolic equation modeling epitaxial thin film growth

Belinda B. King, Oliver Stein and Michael Winkler

Abstract. We study the continuum model for epitaxial thin film growth from [1], 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.

[1] 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)