38 citations · 84 across the 11 of their papers we have counts for
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Interface problems of mixed spatial order
Dionyssios Mantzavinos, Ravindra Pethiyagoda, Dave Smith
We solve interface problems on the line between various constant coefficient linear evolution partial differential equations. Our prototypical examples are the heat, linear Schrödi…
The Airy equation with nonlocal conditions
Bekzod Normatov, David Andrew Smith
We study a third order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the…
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…
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…
Nonlocal and multipoint boundary value problems for linear evolution equations
Beatrice Pelloni, David A Smith
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototyp…
The Linear KdV Equation with an Interface
Bernard Deconinck, Natalie E. Sheils, David A. Smith
The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each doma…
Evolution PDEs and augmented eigenfunctions. Half-line
Beatrice Pelloni, David A. Smith
The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the comp…
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…
Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
David A. Smith
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-spa…