Partial Differential Equations
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.
Autor: | McGhee, Des Picard, Rainer |
---|---|
ISBN: | 9783110250268 |
Auflage: | 1 |
Sprache: | Englisch |
Seitenzahl: | 469 |
Produktart: | Gebunden |
Verlag: | De Gruyter |
Veröffentlicht: | 16.06.2011 |
Untertitel: | A unified Hilbert Space Approach |
Schlagworte: | Evolution Equation Hilbert Space Mathematics Partial Differential Equations Sobolev |
Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK.