Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Subtitle: Including a Solution to Hilbert's Fifth Problem
By: by Elemér E. Rosinger
Series: Mathematics and Its Applications -- 452; Mathematics and Its Applications -- 452
Publisher: Springer Netherlands
Published: 1998
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 238
ISBN-13: 9789048150939; 9789401590761
Subjects: Mathematics; Differential equations, partial; Topological Groups; Global analysis
Description: This book presents global actions of arbitrary Lie groups on large classes of generalised functions by using a novel parametric approach. This new method extends and completes earlier results of the author and collaborators, in which global Lie group actions on generalised functions were only defined in the case of projectable or fibre-preserving Lie group actions. The parametric method opens the possibility of dealing with vastly larger classes of Lie semigroup actions which still transform solutions into solutions. These Lie semigroups can contain arbitrary noninvertible smooth mappings. Thus, they cannot be subsemigroups of Lie groups. Audience: This volume is addressed to graduate students and researchers involved in solving linear and nonlinear partial differential equations, and in particular, in dealing with the Lie group symmetries of their classical or generalised solutions.
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