Sascha Trostorff's Books

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

By: Des McGhee,Rainer Picard,Sascha Trostorff,Marcus Waurick

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A Primer for a Secret Shortcut to PDEs of Mathematical Physics

By: Des McGhee,Rainer Picard,Sascha Trostorff,Marcus Waurick

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.

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Page Count

191

Publisher

Springer Nature

Published Date

ISBN 10

3030473333

ISBN 13

9783030473334

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

By: Des McGhee,Rainer Picard,Sascha Trostorff,Marcus Waurick

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A Primer for a Secret Shortcut to PDEs of Mathematical Physics

By: Des McGhee,Rainer Picard,Sascha Trostorff,Marcus Waurick

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Solve jigsaw puzzle

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Page Count

191

Publisher

Springer Nature

Published Date

ISBN 10

3030473333

ISBN 13

9783030473334

Evolutionary Equations

Picard's Theorem for Partial Differential Equations, and Applications

By: Christian Seifert,Sascha Trostorff,Marcus Waurick

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Evolutionary Equations

Picard's Theorem for Partial Differential Equations, and Applications

By: Christian Seifert,Sascha Trostorff,Marcus Waurick

This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

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Page Count

317

Publisher

Birkhäuser

Published Date

ISBN 10

3030893960

ISBN 13

9783030893965

Book's by Sascha Trostorff

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

A Primer for a Secret Shortcut to PDEs of Mathematical Physics

Evolutionary Equations

Evolutionary Equations

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