3 citations · 7 across the 7 of their papers we have counts for
7 papers
The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 2. The Cauchy problem on a finite interval
D. J. Needham, J. Billingham
In the second part of this series of papers, we address the same Cauchy problem that was considered in part 1, namely the nonlocal Fisher-KPP equation in one spatial dimension, \[…
The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line
D. J. Needham, J. Billingham, N. M. Ladas +1
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \[ u_t = D u_{xx} + u(1-ϕ*u), \] where is a spatial convolution wi…
The Riemann problem for a generalised Burgers equation with spatially decaying sound speed. II General qualitative theory
John Christopher Meyer, David John Needham
We establish that the initial value problem for a generalised Burgers equation considered in part I of this paper, is well-posed. We also establish several qualitative properties o…
The Development of a Wax Layer on the Interior Wall of a Circular Pipe Transporting Heated Oil -- The Effects of Temperature Dependent Wax Conductivity
Sophie Lauren Mason, John Christopher Meyer, David John Needham
In this paper we develop and significantly extend the thermal phase change model, introduced in [12], describing the process of paraffinic wax layer formation on the interior wall…
The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with cut-off Reaction Rate. II. Evolution of Travelling Waves
A. D. O. Tisbury, D. J. Needham, A. Tzella
In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the…
The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data
John Christopher Meyer, David John Needham
In this paper, we establish the existence of spatially inhomogeneous classical self-similar solutions to a non-Lipschitz semi-linear parabolic Cauchy problem with trivial initial d…
On a functional derivative estimate relating to the Cauchy problem for scalar semi-linear parabolic partial differential equations with general continuous nonlinearity
John Christopher Meyer, David John Needham
In this paper, we consider a functional derivative estimate for the first spatial derivative of bounded classical solutions to th…