On Thursday 12th of October at 4pm Martin Wechselberger (University of Sydney) will give a talk in the Amsterdam Dynamics seminar.
The talk will take place in the Maryam seminar room (9A-46) and everyone is welcome to join for drinks at Bar Boele after the talk. Note: the talk takes place on a Thursday!
Title: Generalised shock selection rules in reaction-nonlinear diffusion models: a geometric singular perturbation analysis
Abstract: Reaction-nonlinear diffusion (RND) partial differential equations (PDEs) are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In this talk, I will demonstrate the utility and scope of regularisation as a technique to investigate shock-fronted solutions of RND PDEs, using geometric singular perturbation theory (GSPT) as the main mathematical framework. In particular, I will show that composite regularisations can be used to construct families of shock-fronted travelling waves sweeping out distinct `generalised equal area rules'. Our analysis blends Melnikov methods---in both smooth and piecewise-smooth settings---with GSPT techniques applied to the PDE over distinct spatiotemporal scales.
This is joint work with Bronwyn Bradshaw-Hajek (University of South Australia), Ian Lizarraga and Robby Marangell (University of Sydney).