Student / postdoc PDE seminar: Dynamics of a second order gradient model for phase transitions

Seminar | September 28 | 4:10-5 p.m. | 736 Evans Hall

 Aaron Yip, Purdue University

 Department of Mathematics

We prove in a radially symmetric geometry, the convergence in the sharp interfacial limit, to motion by mean curvature of a second order gradient model for phase transition. This is in spirit similar to the classical Allen-Cahn theory of phase boundary motion. However the corresponding dynamical equation is fourth order thus creating some challenging difficulties for its analysis. A characterization and stability analysis of the optimal profile are performed which are in turn used in the proof of convergence of an asymptotic expansion. (This is joint work with Drew Swartz.)