Mathematical Physics and Harmonic Analysis Seminar
28 September 2007, Bloc 627

Title: Stability analysis of stationary solutions for the 
  Cahn-Hilliard equation
Speaker: Peter Howard, Texas A&M

Abstract:

I will discuss recent results on the stability of stationary
solutions for the Cahn-Hilliard equation in R^d,
d >= 1.  For the case d = 1, there are precisely three
types of non-constant bounded stationary solutions, periodic
solutions, pulse-type (reversal) solutions, and monotonic
transition fronts.  These solutions can be categorized as
follows: the periodic and reversal solutions are both
spectrally unstable, while the transition fronts are
nonlinearly (phase-asymptotically) stable.  The cases
d > 1 are more complicated, and I will discuss what is
known about stationary solutions in these cases.  Particular
emphasis will be placed on planar transition front (or "kink")
solutions.