176 citations · 874 across the 40 of their papers we have counts for
43 papers
Survival, extinction, and interface stability in a two--phase moving boundary model of biological invasion
Matthew J Simpson, Nizhum Rahman, Scott W McCue +1
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes lin…
Exact sharp-fronted solutions for nonlinear diffusion on evolving domains
Stuart T. Johnston, Matthew J. Simpson
Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or su…
Simplified models of diffusion in radially-symmetric geometries
Luke P. Filippini, Matthew J. Simpson, Elliot J. Carr
We consider diffusion-controlled release of particles from -dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the p…
Exact solutions for diffusive transport on heterogeneous growing domains
Stuart T. Johnston, Matthew J. Simpson
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is…
Exact time-dependent solutions of a Fisher-KPP-like equation obtained with nonclassical symmetry analysis
Scott W McCue, Bronwyn H Bradshaw-Hajek, Matthew J Simpson
We consider a family of exact solutions to a nonlinear reaction-diffusion model, constructed using nonclassical symmetry analysis. In a particular limit, the mathematical model app…
The Effect of Geometry on Survival and Extinction in a Moving-Boundary Problem Motivated by the Fisher-KPP Equation
Alexander K. Y. Tam, Matthew J. Simpson
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 alleviates two pra…