6 citations · 6 across the 2 of their papers we have counts for
5 papers
New Revival Phenomena for Linear Integro-Differential Equations
Lyonell Boulton, Peter J. Olver, Beatrice Pelloni +1
We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in the concrete case of three nonlocal equations that aris…
Linear Dispersive Shocks
David Smith, Thomas Trogdon, Vishal Vasan
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear mod…
Revivals and Fractalisation in the Linear Free Space Schrödinger Equation
Peter J Olver, Natalie E Sheils, David A Smith
We consider the one-dimensional linear free space Schrödinger equation on a bounded interval subject to homogeneous linear boundary conditions. We prove that, in the case of pseudo…
The diffusion equation with nonlocal data
Peter D. Miller, David A. Smith
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we spec…
Well-posedness and conditioning of 3rd and higher order two-point initial-boundary value problems
David A. Smith
We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and s…