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A. C. L. Ashton
Researcher at University of Cambridge
Publications - 21
Citations - 183
A. C. L. Ashton is an academic researcher from University of Cambridge. The author has contributed to research in topics: Boundary value problem & Free boundary problem. The author has an hindex of 8, co-authored 21 publications receiving 177 citations.
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A non-local formulation of rotational water waves
TL;DR: In this paper, the Korteweg-de Vries equations of irrotational water waves have been generalized to the case of constant vorticity, as well as the case where the free surface is described by a multivalued function, and a sequence of nearly Hamiltonian systems which provide an approximation in the asymptotic limit of certain physical small parameters.
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On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
TL;DR: In this paper, the central object of the Fokas method is the global relation, which is an integral equation in the spectral Fourier space that couples the given boundary data with the unknown boundary values.
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The spectral Dirichlet-Neumann map for Laplace's equation in a convex polygon
TL;DR: 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 is provided and new proofs of classical results using mainly complex analytic techniques are provided.
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The Spectral Dirichlet--Neumann Map for Laplace's Equation in a Convex Polygon
TL;DR: In this article, the Dirichlet-Neumann map for Laplace's equation on a convex polygon using Fokas' unified method for boundary value problems is studied.
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Elliptic PDEs with constant coefficients on convex polyhedra via the unified method
TL;DR: In this paper, the authors provide a new method to study the classical Dirichlet problem for constant coefficient second order elliptic PDEs on convex polyhedrons, which can be interpreted as the Fourier analogue to the classical boundary integral equations.