8 citations · 27 across the 8 of their papers we have counts for
7 papers · 1 filter
Elliptic boundary value problems in convex polygons with low regularity boundary data via the unified method
A. C. L. Ashton, A. S. Fokas
We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to th…
The spectral Dirichlet-Neumann map for Laplace's equation in a convex polygon
A. C. L. Ashton
We provide a new approach to studying the Dirichlet-Neumann map for Laplace's equation on a convex polygon using Fokas' unified method for boundary value problems. By exploiting th…
Collections of Fluid Loaded Plates: A Nonlocal Approach
Anthony C. L Ashton
We consider the motion of a collection of fluid loaded elastic plates, situated horizontally in an infinitely long channel. We use a new, unified approach to boundary value problem…
A Nonlocal Formulation of Rotational Water Waves
Anthony C. L Ashton, A. S. Fokas
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height…
A Novel Method of Solution for the Fluid Loaded Plate
Anthony C. L Ashton, A. S. Fokas
We study the Cauchy problem associated with the equations governing a fluid loaded plate formulated on either the line or the half-line. We show that in both cases the problem can…
Conservation Laws and Non-Lie Symmetries
Anthony C. L Ashton
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved curre…