Caltech/UCLA Joint Analysis Seminar

UCLA MS 6627

Let us consider a moving interface forced by its mean curvature and a positive periodic forcing term. We investigate the interplay between the mean curvature and the forcing term in the long run. It turns out that the large time behavior of the interface can be characterized by its head speed and tail speed, which depend continuously on its direction of propagation. If these two speeds are equal in all directions, homogenization appears. Otherwise, the interface exhibits long fingers in a certain direction. In the laminar case, these long fingers converge to traveling waves with different speeds. Moreover, there exists a stationary solution of the cylindrical type.