A Unified Approach to Boundary Value Problems: 78 (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 78) - Softcover

Fokas, Athanassios S.

Softcover

ISBN 10: 0898716519 ISBN 13: 9780898716511

Publisher: Society for Industrial and Applied Mathematics, 2008

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 this title

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.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2008
• Language: English
• ISBN 10: 0898716519
• ISBN 13: 9780898716511
• Binding: Paperback
• Number of pages: 356