Most continuum models of epitaxial growth assume that the film height h(x,t) solves a scalar partial differential equation. I shall discuss a different approach, developed recently with Weinan E, Tak Shing Lo, Tim Schulze, and Aaron Yip, involving a coupled system of PDE's -- a Hamilton-Jacobi equation for the film height coupled to a diffusion equation for the "surface adatom density." Though still phenomenological, this model can be motivated by considering finer scale growth laws. With an appropriate nucleation term the model captures the main qualitative features of spiral growth, including slope selection and coarsening. We thus obtain a new possible mechanism for slope selection and coarsening, different from those associated with more traditional growth models.
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