A unified approach to boundary value problems
By: Athanassios S. Fokas.
Series: CBMS-NSF regional conference series in applied mathematics -- 78
Publisher: Society for Industrial and Applied Mathematics
Published: 2008
Place of publication: Philadelphia
Language: eng
Number of pages: 336
ISBN-13: 9780898716511
Subjects: Boundary value problems
Description: This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Notes: Includes bibliographical references and index.
Table of contents: title: A new transform method for linear evolution equations; title: Evolution equations on the half line; title: Evolution equations on the finite interval; title: Asymptotics and a novel numerical technique; title: Analyitic inversion of integrals; title: From PDEs to classical transforms; title: Riemann-Hilbert and d-bar problems; title: The Fourier transform and its variations; title: The inversion of the attenuated radon transform and medical imaging; title: The Dirichlet to Neumann map for a moving boundary; title: Novel integral representations for linear boundary value problems; title: Divergence formulation, the global relation, and lax pairs; title: Rederivation of the integral representations on the half-line and the finite interval; title: The basic elliptic PDEs in a polygonal domain; title: Novel analytical and numerical methods for elliptic PDEs in a convex polygon; title: The new transform method for elliptic PDEs in simple polygonal domains; title: Formulation of Riemann-Hilbert problems; title: A collocation method in the Fourier plane; title: Integrable nonlinear PDEs; title: From linear to integrable nonlinear PDEs; title: Nonlinear integrable PDEs on the half-line; title: Linearizable boundary conditions; title: The generalized Dirichlet to Neumann map; title: Asymptotics of oscillatory Riemann-Hilbert problems.