9 citations · 26 across the 8 of their papers we have counts for
8 papers
Blow up in a periodic semilinear heat equation
Marco Fasondini, John R. King, J. A. C. Weideman
Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and…
Burgers' equation in the complex plane
Daniel J. VandenHeuvel, Christopher J. Lustri, John R. King +2
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following o…
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…
Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: Nonstandard scaling
John R. King, Jakub Köry, Mariya Ptashnyk
In this paper we undertake a multiscale analysis of nutrient uptake by plant root hairs, considering different scale relations between the radius of hairs and the distance between…
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…
Lie symmetries of nonlinear parabolic-elliptic systems and their application to a tumour growth model
Roman Cherniha, Vasyl' Davydovych, John R. King
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the li…