McGhee / Picard / Trostorff A Primer for a Secret Shortcut to PDEs of Mathematical Physics

1. Auflage 2020
ISBN: 978-3-030-47333-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 183 Seiten, eBook

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

McGhee, Des

Picard, Rainer

Trostorff, Sascha

Waurick, Marcus

Inhaltsverzeichnis

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.

Über Autor(innen)

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.