Group Analysis of Differential Equations and Generalized Functions

DOI10.1137/S003614109833450XzbMath0981.46038arXivmath/9912217MaRDI QIDQ4509930

Michael Kunzinger, Michael Oberguggenberger

Publication date: 19 October 2000

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9912217

zbMATH Keywords

distributionsgroup actionssymmetriesgroup analysisdelta wavesColombeau algebrasLie group analysisalgebras of generalized functionsLie symmetries of differential equationsColombeau's's theoryequations involving generalized functions

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (14)

Nonlinear generalized sections of vector bundles ⋮ Group invariants in algebras of generalized functions ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ Point value characterizations and related results in the full Colombeau algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^e(\Omega )}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^d(\Omega )}$\end{document} ⋮ Foundations of the calculus of variations in generalized function algebras ⋮ Internal sets and internal functions in Colombeau theory ⋮ Group invariant Colombeau generalized functions ⋮ Suppleness of the sheaf of algebras of generalized functions on manifolds ⋮ Inversion of Colombeau generalized functions ⋮ PDE and extrafunctions ⋮ Generalized group actions in a global setting ⋮ Pointwise characterizations in generalized function algebras ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory ⋮ Generalized pseudo-Riemannian geometry

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