A model of crystal growth with corner regularization

We investigate a dynamic model of two dimensional crystal growth

described by a forward-backward parabolic equation. The ill-posed

region of the equation describes the motion of corners on the surface.

We analyze a fourth order regularized version of this equation and

show that the dynamical behavior of the regularized corner can be

described by a traveling wave solution. The speed of the wave is found

by rigorous asymptotic analysis. The interaction between multiple

corners will also be presented together with numerical simulations.

This is joint work in progress with Fang Wan.