Biological invasion, whereby populations of motile and proliferative individuals lead to
moving fronts that invade vacant regions, is routinely studied using partial differential …

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which
involves solving the Fisher–KPP equation on a compactly-supported region with a moving …

Abstract The Fisher–Kolmogorov–Petrovsky–Piskunov (KPP) model, and generalizations
thereof, involves simple reaction–diffusion equations for biological invasion that assume …

This review provides open-access computational tools that support a range of mathematical
approaches to analyse three related scalar reaction-diffusion models used to study …

Abstract The Fisher–Stefan model involves solving the Fisher–KPP equation on a domain
whose boundary evolves according to a Stefan-like condition. The Fisher–Stefan model …

The Fisher–Kolmogorov–Petrovsky–Piskunov model, also known as the Fisher–KPP model,
supports travelling wave solutions that are successfully used to model numerous invasive …

Single-species reaction–diffusion equations, such as the Fisher–KPP and Porous-Fisher
equations, support travelling wave solutions that are often interpreted as simple …

In an earlier work (Berestycki et al., 2013), we introduced a parabolic system to describe
biological invasions in the presence of a line (the “road”) with a specific diffusion, included in …

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 …

A family of travelling wave solutions to the Fisher–KPP equation with speeds c=±5∕ 6 can
be expressed exactly using Weierstra ß elliptic functions. The well-known solution for c= 5∕ …