A unified approach to boundary value problems / Athanassios S. Fokas.

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Bibliographic Details
Uniform Title:CBMS-NSF regional conference series in applied mathematics ; 78.
Main Author: Fokas, A. S., 1952-
Language:English
Published: Philadelphia, PA : Society for Industrial and Applied Mathematics, [2008], ©2008.
Series:CBMS-NSF regional conference series in applied mathematics ; 78.
Subjects:
Boundary value problems.
Physical Description:xv, 336 pages : illustrations (some color) ; 25 cm.
Format: Book
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.