An Interdisciplinary Journal

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

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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Last updated: *April 21, 2003*