16 citations · 16 across the 4 of their papers we have counts for
4 papers
Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity
Thomas Miller, Alexander K. Y. Tam, Robert Marangell +2
Reaction-diffusion equations (RDEs) model the spatiotemporal evolution of a density field according to diffusion and net local changes. Usually, the diffusivity is p…
A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models
Bronwyn H Bradshaw-Hajek, Ian Lizarraga, Robert Marangell +1
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In t…
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…
Exact nonclassical symmetry solutions of Arrhenius reaction-diffusion
P. Broadbridge, B. H. Bradshaw-Hajek, D. Triadis
Exact solutions for nonlinear Arrhenius reaction-diffusion are constructed in dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term le…