3 papers
math.AP2022
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…
math.AP2020
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 (…
math.AP2019
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…