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A unified approach to boundary value problems

Author: A S Fokas
Publisher: Philadelphia, PA : Society for Industrial and Applied Mathematics, ©2008.
Series: CBMS-NSF regional conference series in applied mathematics, 78.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
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Additional Physical Format: Online version:
Fokas, A.S., 1952-
Unified approach to boundary value problems.
Philadelphia, PA : Society for Industrial and Applied Mathematics, ©2008
(OCoLC)654524507
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A S Fokas
ISBN: 9780898716511 0898716519
OCLC Number: 222250960
Description: xv, 336 pages : illustrations (some color) ; 25 cm.
Contents: A new transform method for linear evolution equations --
Evolution equations on the half line --
Evolution equations on the finite interval --
Asymptotics and a novel numerical technique --
Analytical inversion of integrals --
From PDEs to classical transforms --
Riemann-Hilbert and d-bar problems --
The Fourier transform and its variations --
The inversion of the attenuated radon transform and medical imaging --
The Dirichlet to Neumann map for a moving boundary --
Novel integral representations for linear boundary value problems --
Divergence formulation, the global relation, and lax pairs --
Rederivation of the integral representations on the half-line and the finite interval --
The basic elliptic PDEs in a polygonal domain --
Novel analytical and numerical methods for elliptic PDEs in a convex polygon --
The new transform method for elliptic PDEs in simple polygonal domains --
Formulation of Riemann-Hilbert problems --
A collocation method in the Fourier plane --
Integrable nonlinear PDEs --
From linear to integrable nonlinear PDEs --
Nonlinear integrable PDEs on the half-line --
Linearizable boundary conditions --
The generalized Dirichlet to Neumann map --
Asymptotics of oscillatory Riemann-Hilbert problems.
Series Title: CBMS-NSF regional conference series in applied mathematics, 78.
Responsibility: Athanassios S. Fokas.
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Abstract:

This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.

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