Parametric Lie Group Actions On Global Generalised Solutions Of Nonlinear Pdes
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Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Author: Elemer E. Rosinger
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
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.
Nonlinear Theory of Generalized Functions
Author: Michael Oberguggenberger
language: en
Publisher: Routledge
Release Date: 2022-02-27
Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.
Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs
Author: Elemer Elad Rosinger
language: en
Publisher: Springer Science & Business Media
Release Date: 1998-10-31
Presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalized functions. This work addresses those who are interested in solving nonlinear PDEs, and in particular, in studying the Lie group symmetries of their classical or generalized solutions. This new method extends and completes earlier results of the author and collaborators, in which global Lie group actions on generalized functions were only defined in the case of projectable or fiber preserving Lie group actions. Annotation copyrighted by Book News, Inc., Portland, OR