March 27, 2009:  Amy Novick-Cohen, Technion-IIT, Haifa

Coupled surface diffusion and motion by mean curvature
  

  Problems entailing coupled surface diffusion and motion by mean curvature arise naturally in various contexts in materials science. It can be considered as a simplified description for sintering processes, and it arises also in describing the evolution of thin films and their stability. From the point of view of mathematical modeling, coupled surface diffusion and motion by mean curvature can be obtained formally as the hydrodynamical limit from a coupled system of Allen-Cahn and Cahn-Hilliard equations. While motion by mean curvature has been verified as a limiting motion obtainable from the Allen-Cahn equation, so far there exists only a formal connection between surface diffusion and the Cahn-Hilliard equation. Some of the formal limits which would be interesting to verify will be explained, as shall a certain connection with wetting. Various special solutions and stability properties of the coupled motion will also be discussed.