Front propagation in two-component reaction-diffusion systems with cut-off functions #

Panagiotis Kaklamanos, Tasso Kaper, Nikola Popovic

14:30 Tuesday in 4Q04.

Part of the Travelling waves session.

Abstract #

The Fisher-Kolmogorov-Petrowskii-Piscounov (FKPP) equation with a cut-off was popularised by Brunet and Derrida in the 1990s as a model for many-particle systems in which concentrations below a given threshold are not attainable. While travelling wave solutions in cut-off scalar reaction-diffusion equations have since been studied extensively, the impacts of a cut-off on systems of such equations are less well understood. As a step towards a broader understanding, we consider a general FKKP-type system with a cut-off in both components that is motivated by models for the spatial spread of hitchhiking traits. Our focus is on the existence, structure, and stability of travelling fronts, as well as on their dependence on model parameters; in particular, we address the correction to the front propagation speed that is due to the cut-off. Our analysis is for the most part based on a combination of geometric singular perturbation theory and the desingularisation technique known as “blow-up”.