A Primer for a Secret Shortcut to PDEs of Mathematical Physics (Frontiers in Mathematics)
Language: English
Published by Springer (India) Private Limited, 2020
- Softcover
- New
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- Title
- A Primer for a Secret Shortcut to PDEs of Mathematical Physics (Frontiers in Mathematics)
- Author
- McGhee, Des; Picard, Rainer; Trostorff, Sascha; Waurick, Marcus
- Publisher
- Springer (India) Private Limited
- Publication year
- 2020
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 3030473325
- ISBN 13
- 9783030473327
- Series
- Book 46 of 48: Frontiers in Mathematics
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.
"Synopsis" may belong to another edition of this title.
About the Author
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.
"About the title" may belong to another edition of this title.
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