March 27, 2009: Amy NovickCohen, TechnionIIT, 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 AllenCahn and CahnHilliard equations. While motion by mean
curvature has been verified as a limiting motion obtainable from the
AllenCahn
equation, so far there exists only a formal connection between surface
diffusion
and the CahnHilliard 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.
