3 papers
math.AP2023
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…
math.DS2023
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…
nlin.SI2022
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…