A Primer for a Secret Shortcut to PDEs of Mathematical Physics (Frontiers in Mathematics) - Softcover

McGhee, Des; Picard, Rainer; Trostorff, Sascha; Waurick, Marcus

Softcover

ISBN 10: 3030473325 ISBN 13: 9783030473327

Publisher: Birkhäuser, 2020

Synopsis

​This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach.

The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

About this title

About the Author

Des McGhee is Honorary Lecturer at the University of Strathclyde in Glasgow, Scotland.

Rainer Picard is Seniorprofessor at the TU Dresden in Germany.

Sascha Trostorff is lecturer at the Christian-Albrechts-Universität zu Kiel in Germany.

Marcus Waurick Chancellor's Fellow at the University of Strathclyde in Glasgow, Scotland.

From the Back Cover

This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering. As a unique feature, this powerful tool for tackling time-dependent partial differential equations is subsequently applied to many equations. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. 

The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in the appendix. The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.

Edition details

• Publisher: Birkhäuser
• Publication date: 2020
• Language: English
• ISBN 10: 3030473325
• ISBN 13: 9783030473327
• Binding: Paperback
• Edition number: 1
• Number of pages: 193