Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization (Q2346745)

In this study, the authors approach the morphologic evolution of anisotropic, epitaxially strained films driven by stress and surface mass transport in three dimensions. The study can be considered as the evolutionary counterpart of the static theory developed in the two-dimensional case and in three dimensions. The two-dimensional formulation of the same evolution problem has been addressed previously for the case of motion by evaporation-condensation. The authors consider that the physical setting behind the evolution equation is that the free interface is allowed to evolve via surface diffusion under the influence of a chemical potential. Assuming that mass transport in the bulk occurs at a much faster time scale, and thus can be neglected, it may be considered, according to the Einstein-Nernst relation, that the evolution is governed by the so called ``volume-preserving equation''. We must emphasize several issues addressed.{\parindent=0.6cm\begin{itemize}\item[1.] The introduction of the discrete time evolutions; \item[2.] Proof of a local-in-time existence result; \item[3.] The use of minimizing movements in the context of higher-order geometric flows; \item[4.] The Liapunov stability of the flat configuration, corresponding to a horizontal profile. \end{itemize}}