7 citations · 14 across the 8 of their papers we have counts for
8 papers
A heterogeneous nonlocal advection--diffusion system
Joseph McCusker, John Christopher Meyer, Mabel Lizzy Rajendran
We present a self-contained investigation on the local and global well-posedness for a system of nonlocal advection--diffusion equations for a heterogeneous population over $\mathb…
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…
Comparison principles for a class of nonlinear non-local integro-differential operators on unbounded domains
Nikolaos Michael Ladas, John Christopher Meyer
We present extensions of the comparison and maximum principles available for nonlinear non-local integro-differential operators $P:\mathcal{C}^{2,1}(Ω\times (0,T])\times L^\infty (…
A note on boundary point principles for partial differential inequalities of elliptic type
John Christopher Meyer
In this note we consider boundary point principles for partial differential inequalities of elliptic type. Firstly, we highlight the difference between conditions required to estab…
On two-signed solutions to a second order semi-linear parabolic partial differential equation with non-Lipschitz nonlinearity
Victoria Clark, John Christopher Meyer
In this paper, we establish the existence of a 1-parameter family of spatially inhomogeneous radially symmetric classical self-similar solutions to a Cauchy problem for a semi-line…
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…