Analysis/CAM Seminar: Connor Smith (Kansas) ": Metastable Traveling Fronts - N.A. - (Laramie, WY)

RH247 Friday, February 2, 2018, 4:10 – 5pm We study an equation that models ripple formation when a flat surface is bombarded by an ion beam. The experimentally observed ripples consist of parts with a certain positive slope, parts with a certain negative slope, and transitions between the 2 slopes. The transitions may be modeled as traveling fronts with stable point spectrum but unstable essential spectrum. At 1st glance this may be written off as “unstable.” However numerical results suggest that the instability has 2 parts; a convecting part that saturates to some value and an exponentially decaying part that slightly modulates the underlying transition. We define an exponential weight that decays in the direction the 1st part of the instability travels in, allowing us to focus on the 2nd part of the instability. In this exponentially weighted space we obtain a linear stability result.