Des McGhee's Books

Partial Differential Equations

A unified Hilbert Space Approach

By: Rainer Picard,Des McGhee

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Partial Differential Equations

A unified Hilbert Space Approach

By: Rainer Picard,Des McGhee

This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.

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Page Count

489

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110250276

ISBN 13

9783110250275

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

Age

Page Count

191

Publisher

Springer Nature

Published Date

ISBN 10

3030473333

ISBN 13

9783030473334

Partial Differential Equations

A unified Hilbert Space Approach

By: Rainer Picard,Des McGhee

Write a review Read reviews Take a Quiz Solve Book Puzzle

Partial Differential Equations

A unified Hilbert Space Approach

By: Rainer Picard,Des McGhee

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

489

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110250276

ISBN 13

9783110250275

Book's by Des McGhee

Partial Differential Equations

Partial Differential Equations

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

Partial Differential Equations

Partial Differential Equations

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