3 papers
math.AP2024
Shock selection in reaction--diffusion equations with partially negative diffusivity using nonlinear regularisation
Thomas Miller, Alexander K. Y. Tam, Robert Marangell +2
We consider a general reaction--nonlinear-diffusion equation with a region of negative diffusivity, and show how a nonlinear regularisation selects a shock position. Negative diffu…
q-bio.PE2024
Front stability of infinitely steep travelling waves in population biology
Matthew J Simpson, Nizhum Rahman, Alexander KY Tam
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Man…
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…