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Mathematics and Its Applications Ser.: Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDES and a Solution to Hilbert's Fifth Problem by Elemer E. Rosinger (1998, Hardcover)

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Number of Pages: 238. Weight: 1.19 lbs. Publication Date: 1998-10-31. Publisher: Springer.

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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.

Product Identifiers

Publisher
Springer Netherlands
ISBN-10
0792352327
ISBN-13
9780792352327
eBay Product ID (ePID)
642680

Product Key Features

Author
Elemer E. Rosinger
Publication Name
Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDES and a Solution to Hilbert's Fifth Problem
Format
Hardcover
Language
English
Series
Mathematics and Its Applications Ser.
Publication Year
1998
Type
Textbook
Number of Pages
Xviii, 238 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
42.3 Oz

Additional Product Features

Series Volume Number
452
Number of Volumes
1 Vol.
Lc Classification Number
Qa370-380
Reviews
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, E.E. RosingerParametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEsIncluding 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, 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, E.E. Rosinger Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilberta'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." a?MATHEMATICAL REVIEWS
Table of Content
1. Introduction.- 2. Actions on functions, difficulties.- 3. Parametric representation of functions.- 4. Action on parametric representations.- 5. Parametric functions as solutions.- 6. Rarefaction waves and Riemann solvers of the nonlinear shock wave equation.- 7. Arbitrary nonlinear Lie group actions on generalised functions.- 8. Nonprojectable Lie group symmetries of rarefaction waves and Riemann solvers.- 9. General parametric approach to Lie symmetries.- 10. Projectable Lie group actions and Hilbert's fifth problem.- 11. Nonprojectable Lie group actions and an answer to Hilbert's fifth problem.- 12. Singularities and the nowhere dense algebras of generalised functions.- 13. Lie semigroup actions and semisymmetries.
Copyright Date
1998
Topic
Group Theory, Differential Equations / General, Mathematical Analysis
Lccn
98-034116
Dewey Decimal
515/.353
Intended Audience
Scholarly & Professional
Dewey Edition
21
Illustrated
Yes
Genre
Mathematics

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Mathematics and Its Applications Ser.: Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDES and a Solution to Hilbert's Fifth Problem by Elemer E. Rosinger (1998, Hardcover)

About this product

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item 1 Parametric Lie Group Actions On Global Generalised Solutions Of Nonlinear P...

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Best Selling in Textbooks

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