# Meeting Details

Title: Stability analysis of stationary solutions for the Cahn-Hilliard Equation * Computational and Applied Mathematics Colloquium Peter Howard (TAMU) I will discuss recent results on the stability of stationary solutions for the Cahn-Hilliard equation in $\mathbb{R}^d$, $d \ge 1$. 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 $d \ge 2$ 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.