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Athanassios S. Fokas - Unified Approach to Boundary Value Problems - 9780898716511 - V9780898716511
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Unified Approach to Boundary Value Problems

€ 136.52
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Description for Unified Approach to Boundary Value Problems Paperback.
Presents a new approach to analyzing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, a method that the author first introduced in 1997 and which is based on ideas of the inverse scattering transform. This method is unique in also yielding novel integral representations for the explicit solution of linear boundary value problems, which include such classical problems as the heat equation on a finite interval and the Helmholtz equation in the interior of an equilateral triangle.

The author’s thorough introduction allows the interested reader to quickly assimilate the essential results of the book, avoiding many computational details. 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; 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.

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.
  • Integrable nonlinear PDEs.

    Product Details

    Format
    Paperback
    Publication date
    2008
    Publisher
    Society for Industrial & Applied Mathematics,U.S. United States
    Number of pages
    356
    Condition
    New
    Number of Pages
    351
    Place of Publication
    New York, United States
    ISBN
    9780898716511
    SKU
    V9780898716511
    Shipping Time
    Usually ships in 7 to 11 working days
    Ref
    99-37

    About Athanassios S. Fokas
    Athanassios S. Fokas is Professor of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. In 2000 he was awarded the Naylor Prize for his work on which this book is based. In 2006 he received the Excellence Prize of the Bodossaki Foundation.

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