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mcghee des; picard rainer; trostorff sascha; waurick marcus - a primer for a secret shortcut to pdes of mathematical physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 08/2020
Edizione: 1st ed. 2020





Trama

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.





Sommario

Introduction.- The Solution Theory for a Basic Class of Evolutionary Equations.- Some Applications to Models from Physics and Engineering.- But what about the Main Stream?.- Two Supplements for the Toolbox.- Requisites from Functional Analysis.




Autore

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.












Altre Informazioni

ISBN:

9783030473327

Condizione: Nuovo
Collana: Frontiers in Mathematics
Dimensioni: 240 x 168 mm Ø 454 gr
Formato: Brossura
Illustration Notes:X, 183 p. 8 illus. in color.
Pagine Arabe: 183
Pagine Romane: x


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