LONG TIME BEHAVIOR OF SURFACE DIFFUSION OFANISOTROPIC SURFACE ENERGY
We investigate the surface diffusion flow of smooth curves with anisotropic surface energy.
This geometric flow is the H−1-gradient flow of an energy functional. It preserves the area
enclosed by the evolving curve while at the same time decreases its energy. We show the
existence of a unique local in time solution for the flow but also the existence of a global in
time solution if the initial curve is close to the Wulff shape. In addition, we prove that the
global solution converges to the Wulff shape as t → ∞. In the current setting, the anisotropy
is not too strong so that the Wulff shape is given by a smooth curve. In the last section, we
formulate the corresponding problem when the Wulff shape exhibits corners.
- Doctor of Philosophy
- West Lafayette