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 …

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

Reaction–diffusion equations (RDEs) are often derived as continuum limits of lattice-based
discrete models. Recently, a discrete model which allows the rates of movement …

Mechanical cell competition is important during tissue development, cancer invasion, and
tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can …

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 …