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A Unified Approach to Boundary Value Problems

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A Unified Approach to Boundary Value Problems
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A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

Informacija

Autorius: Athanassios S. Fokas
Leidėjas: Society for Industrial and Applied Mathematics
Išleidimo metai: 2008
Knygos puslapių skaičius: 356
ISBN-13: 9780898716511
Formatas: 7 x 0.75 x 10 inches. Knyga minkštu viršeliu
Kalba: Anglų

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