A moving-boundary model for biological invasion and recession in two dimensions
Date:
Abstract: This seminar summarises work undertaken while I was a postdoc supervised by Prof. Mat Simpson at QUT. The research concerns the Fisher–Stefan model for biological invasion and recession. The Fisher–Stefan model involves solving the Fisher–KPP equation on a moving domain that evolves according to a Stefan-like condition. Unlike the Fisher–KPP equation, the Fisher–Stefan model explicitly defines the interface between occupied and unoccupied regions, and admits solutions where the population recedes. Recent PhD graduate Dr. Maud El-Hachem (with Mat and Prof. Scott McCue) analysed survival–extinction conditions and travelling wave solutions in the Fisher–Stefan model and related models in one spatial dimension. My research project explored survival–extinction and travelling wave solutions in two spatial dimensions. We first investigated the effect of geometry on survival and extinction, before considering the stability of advancing and receding planar fronts to transverse shape perturbations. I will outline results from these investigations in my seminar.