Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs : Including a Solution to Hilbert's Fifth Problem
Language: English
Published by Springer Netherlands, 1998
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Druck auf Anfrage Neuware - Printed after ordering - This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group actions were defined globally - in the projectable case - on the nowhere dense differential algebras of generalised functions An, as well as on the Colombeau algebras of generalised functions, and also on the spaces obtained through the order completion of smooth functions, spaces which contain the solutions of arbitrary continuous nonlinear PDEs. Further details can be found in Rosinger & Rudolph, and Rosinger & Walus [1,2]. To the extent that arbitrary Lie group actions are now defined on such nonsmooth entities as generalised functions, this result can be seen as giving an ans wer to Hilbert's fifth problem, when this problem is interpreted in its original full gener ality, see for details chapter 11.
Seller Inventory # 9780792352327
- Title
- Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs : Including a Solution to Hilbert's Fifth Problem
- Author
- Elemer E. Rosinger
- Publisher
- Springer Netherlands
- Publication year
- 1998
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0792352327
- ISBN 13
- 9780792352327
- Item weight
- 507 grams
- Dimensions
- 241x160x20 mm
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Review
E.E. Rosinger
Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Including a Solution to Hilbert’s Fifth Problem
"This book presents a novel approach to Lie group actions on ordinary and generalized functions, based on parametric representation. This allows a global definition of arbitrary nonlinear Lie group actions on functions, including generalized functions. The parametric approach also makes possible a global definition for Lie semigroup actions. It is shown that the usual Lie group symmetries of classical solutions of smooth nonlinear PDEs will remain Lie group symmetries of generalized solutions of such equations."
―MATHEMATICAL REVIEWS
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