Two–dimensional linear partial differential equations in a convex polygon

By A. S. Fokas. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001

127 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011, background): “…a decade ago, Fokas and collaborators introduced a new analytical transform technique that provides closed-form solutions (in terms of contour integrals) for a variety of PDE boundary value (BV) and initial-boundary value (IBV) problems (Fokas 1997, 2001, 2002, Fokas & Pelloni 2005; Spence 2010).”
Explicit integral solutions for the plane elastostatic semi-strip (2004, methodology): “A general methodology for treating corner singularities is described in respect of the Laplace equation in Fokas & Kapaev (2003). There exist two ‘sources’ of singularities: one is ‘external’ and is due to a lack of smoothness of the given boundary conditions; the other is ‘internal’ and depends on ”
The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations (2005, methodology): “In the past few years, a method for solving boundary-value problems for linear evolution PDEs was proposed by Fokas (2001).”