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Unified Approach to Boundary Value Problems
Athanassios S. Fokas
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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:
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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