Table of Contents for: A unified approach to boundary value pro

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A unified approach to boundary value problems [electronic resource] /

Athanassios S. Fokas.

Book Cover
Main Author: Fokas, A. S.
Published: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2008.
Series: CBMS-NSF regional conference series in applied mathematics ; 79.
Topics: Boundary value problems.
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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 -- Analyitic 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.

Table of Contents for: A unified approach to boundary value pro