Nonlinear Phenomena in Complex Systems, 2003, Vol.6, No.1, pp.582-591

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2003, Vol.6, No.1, pp.582-591

On Solutions of Certain Classes of Evolution Equations for Surface Morphologies
R.H.W. Hoppe, W.G. Litvinov, and S.J. Linz

We introduce a generalization of a known evolution equation of surface morphologies developed in [6,11,12]. For this generalized equation, initial boundary value problems are studied for periodical boundary conditions as well as for Dirichlet boundary conditions. We prove the existence of weak solutions of these problems for an arbitrary finite interval of time. For the case of smooth data and Dirichlet boundary conditions, the existence of a unique smooth solution is established.
Key words: surface, evolution, solution, smoothness

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