A Unified Approach to Boundary Value Problems

Athanassios S Fokas

ISBN 10: 0898716519 / ISBN 13: 9780898716511

Published by Society For Industrial And Applied Mathematics (SIAM) Nov 2008, 2008

About this Item

Neuware - 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.

Seller Inventory # 9780898716511

Bibliographic Details

• Title: A Unified Approach to Boundary Value Problems
• Publisher: Society For Industrial And Applied Mathematics (SIAM) Nov 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 0898716519
• ISBN 13: 9780898716511
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 172H x 24D millimeters 254 millimeters width by 172 millimeters height by 24 millimeters depth
• Weight: 563 grams

About this title

Synopsis

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.

About the Author

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.