Partial Differential Equations

A unified Hilbert Space Approach
1. Auflage 2011
ISBN: 978-3-11-025026-8
Verlag: De Gruyter

Buch, Englisch, Band 55, 469 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 999 g

Reihe: De Gruyter Expositions in Mathematics

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.

Zielgruppe

Students, Reseachers; Academic Libraries

Autoren/Hrsg.

Mcghee, Des

Picard, Rainer

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Frontmatter
Preface
Contents
Nomenclature
Chapter 1 Elements of Hilbert Space Theory
Chapter 2 Sobolev Lattices
Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ? N
Chapter 4 Linear Evolution Equations
Chapter 5 Some Evolution Equations of Mathematical Physics
Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics
Conclusion
Bibliography
Index

Über Autor(innen)

Mcghee, Des
Des McGhee, University of Strathclyde, Glasgow, Scottland, UK.

Picard, Rainer
Rainer Picard, Dresden University of Technology, Germany;

Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK.