| Partial Differential Equations: A Unified Hilbert Space Approach Contributor(s): Picard, Rainer (Author), McGhee, Des (Author) |
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ISBN: 3110250268 ISBN-13: 9783110250268 Publisher: de Gruyter OUR PRICE: $285.00 Product Type: Hardcover - Other Formats Published: June 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Transformations - Mathematics | Differential Equations - General - Mathematics | Mathematical Analysis |
| Dewey: 515.733 |
| LCCN: 2011004423 |
| Physical Information: 1.06" H x 6.69" W x 9.61" (2.14 lbs) 487 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics. |
Contributor Bio(s): Picard, Rainer: - Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK. |