A Primer for a Secret Shortcut to PDEs of Mathematical Physics / by Des McGhee, Rainer Picard, Sascha Trostorff, Marcus Waurick

By:

McGhee, Des F [VerfasserIn]

Contributor(s):

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Frontiers in Mathematics | Springer eBook CollectionPublisher: Cham : Springer International Publishing, 2020Publisher: Cham : Imprint: Birkhäuser, 2020Edition: 1st ed. 2020Description: 1 Online-Ressource(X, 183 p. 8 illus. in color.)ISBN:

9783030473334

Subject(s):

Partial differential equations

Additional physical formats: 9783030473327 | 9783030473341 | Erscheint auch als: A primer for a secret shortcut to PDEs of mathematical physics. Druck-Ausgabe Cham, Switzerland : Birkhäuser, 2020. x, 183 Seiten | Erscheint auch als: 9783030473341 Druck-AusgabeDDC classification:

515.353 23

RVK: RVK: SK 540DOI: DOI: 10.1007/978-3-030-47333-4Online resources:

Summary: 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.Summary: 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.PPN: PPN: 1728471583Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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