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Travelling waves, blow-up and extinction in the Fisher-Stefan model by McCue, Scott W.; El-Hachem, Maud; Simpson, Matthew J. is a scholarly article available to read on EtoBox.

What is Travelling waves, blow-up and extinction in the Fisher-Stefan model about?

While there is a long history of employing moving boundary problems in physics, in particular via Stefan problems for heat conduction accompanied by a change of phase, more recently such approaches have been adapted to study biological invasion. For example, when a logistic growth term is added to the governing partial differential equation in a Stefan problem, one arrives at the Fisher-Stefan model, a generalisation of the well-known Fisher-KPP model, characterised by a leakage coefficient $\kappa$ which relates the speed of the moving boundary to the flux of population there. This Fisher-Stefan model overcomes one of the well-known limitations of the Fisher-KPP model, since time-dependent solutions of the Fisher-Stefan model involve a well-defined front with compact support which is more natural in terms of mathematical modelling. Almost all of the existing analysis of the standard Fisher-Stefan model involves setting $\kappa > 0$, which can lead to either invading travelling wave solutions or complete extinction of the population. Here, we demonstrate how setting $\kappa < 0$ leads to retreating travelling waves and an interesting transition to finite-time blow-up. For certain i

Author

McCue, Scott W.; El-Hachem, Maud; Simpson, Matthew J.

Published

2021

Language

EN