Pushmi-pullyu fronts and population dynamics
Invasions in population dynamics are often characterized as either
pushed' orpulled.' Biologically this is related to the Allee affect, while mathematically, this distinction is whether the front is driven by nonlinear dynamics at the front (pushed) versus linear dynamics beyond the front (pulled). In this talk, I will present a family of models in which an intermediate `pushmi-pullyu' behavior occurs. The analysis of these models is delicate as both the nonlinear dynamics at the front and linear dynamics beyond the front play nontrivial roles. The goal of the talk is to connect disparate models (taxis, combustion, probabilistic) in this context as well as to display a few of the mathematical tools used in their study such as a new weighted Nash inequality.