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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…
math.AP2024
Stability of asymptotic waves in the Fisher-Stefan equation
T. T. H. Bui, P. van Heijster, R. Marangell
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonl…
math.AP2014
Dynamical Hamiltonian-Hopf instabilities of periodic traveling waves in Klein-Gordon equations
Robert Marangell, Peter D. Miller
We study the unstable spectrum close to the imaginary axis for the linearization of the nonlinear Klein-Gordon equation about a periodic traveling wave in a co-moving frame. We def…