3 papers
math.AP2020
Asymptotic Analysis of a Two-Phase Model of Solid Tumour Growth
Andrea Genovese de Oliveira, John R. King
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, Kin…
physics.flu-dyn2019
Moving boundary problems for quasi-steady conduction limited melting
Liam C. Morrow, John R. King, Timothy J. Moroney +1
The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that the cr…
math.AP2016
Pattern formation in a pseudo-parabolic equation
C. M. Cuesta, J. R. King
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished a…