Authors:
- Presents a way of solving PDEs with very little theory
- Provides required background knowledge in the appendix
- Appeals to students and researchers alike
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK
Des McGhee, Marcus Waurick
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Institut für Analysis, TU Dresden, Dresden, Germany
Rainer Picard
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Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
Sascha Trostorff
About the authors
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.
Bibliographic Information
Book Title: A Primer for a Secret Shortcut to PDEs of Mathematical Physics
Authors: Des McGhee, Rainer Picard, Sascha Trostorff, Marcus Waurick
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-030-47333-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-47332-7Published: 25 August 2020
eBook ISBN: 978-3-030-47333-4Published: 24 August 2020
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: X, 183
Number of Illustrations: 8 illustrations in colour
Topics: Partial Differential Equations