In this short survey, we describe some recent developments on the modeling of propagation
by reaction-differential equations with free boundaries, which involve local as well as …

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 …

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∕ …

We consider a moving boundary mathematical model of biological invasion. The model
describes the spatiotemporal evolution of two adjacent populations: each population …

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

Abstract Models of diffusive processes that occur on evolving domains are frequently
employed to describe biological and physical phenomena, such as diffusion within …

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 …

Fixed and moving boundary problems for the one-dimensional heat equation are
considered. A unified approach to solving such problems is proposed by embedding a given …

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 …

The nonlinear Fisher-KPP diffusion-reaction equation has been successfully employed to
model competitive processes in biological populations. A robust numerical method for …