Parametric Lie group actions on global generalised solutions of nonlinear PDEs : including a solution to Hilbert's fifth problem

by Elemér E. Rosinger

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[目次]

  • Preface. 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. Appendix. References. Index.

「Nielsen BookData」より

[目次]

  • Preface. 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. Appendix. References. Index.

「Nielsen BookData」より

この本の情報

書名 Parametric Lie group actions on global generalised solutions of nonlinear PDEs : including a solution to Hilbert's fifth problem
著作者等 Rosinger, Elemer E.
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic
刊行年月 c1998
版表示 1st ed. Softcover of orig. ed. 1998
ページ数 xvii, 234 p.
大きさ 24-25 cm
ISBN 0792352327
9789048150939
NCID BA3842083X
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言語 英語
出版国 オランダ
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