An analysis of crystalline surface diffusion in the framework of subdifferential method
Thitarie Rungratgasame · Purdue e-Pubs (Purdue University System) · 2012
We refer to the work of Carter-Roosen-Cahn-Taylor in 1994 about crystalline motion by surface diffusion. They formulate the evolution of polygonal curves as the gradient flow of a crystalline surface energy with respect to the H–1 inner product. This leads to our study to clarify their formulation in terms of the canonical restriction of the surface energy subdifferential. We establish a new but related energy functional and rigorously characterize its subdifferential and canonical restriction. This is used to formulate the evolution of the crystal boundary. Moreover, the formulation leads us to an interesting feature in the surface diffusion which is the splitting of facets. We can derive a catalog of all possible minimizers afterward. As a comparison, we also study the H–1 negative gradient flow derived from the total variation norm which is related to a fourth order singular equation.