Group analysis of differential equations and generalized functions

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dc.creatorKunzinger, Michael
dc.creatorOberguggenberger, Michael
dc.date1999-12-28
dc.date.accessioned2026-07-07T05:32:31Z
dc.date.available2026-07-07T05:32:31Z
dc.descriptionWe present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau's theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions remain symmetries for generalized solutions. Moreover, we introduce a generalization of the infinitesimal methods of group analysis that allows to compute symmetries of linear and nonlinear differential equations containing generalized function terms. Thereby, the group generators and group actions may be given by generalized functions themselves.
dc.description27 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/9912217
dc.identifierhttp://arxiv.org/abs/math/9912217
dc.identifierSIAM J. Math. Anal. 31 (2000) no. 6, 1192-1213.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79684
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject46F30; 35Dxx; 35A30; 58G35
dc.titleGroup analysis of differential equations and generalized functions
dc.typetext

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