Nonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation

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MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (Unesp)-
Autor(es): dc.contributorUniversidade Estadual de Campinas (UNICAMP)-
Autor(es): dc.creatorda Silva, P. R. [UNESP]-
Autor(es): dc.creatorMeza-Sarmiento, I. S. [UNESP]-
Autor(es): dc.creatorNovaes, D. D.-
Data de aceite: dc.date.accessioned2022-02-22T00:29:34Z-
Data de disponibilização: dc.date.available2022-02-22T00:29:34Z-
Data de envio: dc.date.issued2020-12-11-
Data de envio: dc.date.issued2020-12-11-
Data de envio: dc.date.issued2019-12-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1007/s12591-018-0439-1-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/200147-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/200147-
Descrição: dc.descriptionWe consider piecewise smooth vector fields (PSVF) defined in open sets M⊆ Rn with switching manifold being a smooth surface Σ. We assume that M\ Σ contains exactly two connected regions, namely Σ + and Σ -. Then, the PSVF are given by pairs X= (X+, X-) , with X= X+ in Σ + and X= X- in Σ -. A regularization of X is a 1-parameter family of smooth vector fields Xε, ε> 0 , satisfying that Xε converges pointwise to X on M\ Σ , when ε→ 0. Inspired by the Fenichel Theory, the sliding and sewing dynamics on the discontinuity locus Σ can be defined as some sort of limit of the dynamics of a nearby smooth regularization Xε. While the linear regularization requires that for every ε> 0 the regularized field Xε is in the convex combination of X+ and X-, the nonlinear regularization requires only that Xε is in a continuous combination of X+ and X-. We prove that, for both cases, the sliding dynamics on Σ is determined by the reduced dynamics on the critical manifold of a singular perturbation problem. We apply our techniques in the description of the nonlinear regularization of normal forms of PSVF in R2 and in R3.-
Descrição: dc.descriptionDepartamento de Matemática IBILCE-UNESP, Rua C. Colombo, 2265-
Descrição: dc.descriptionDepartamento de Matemática Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz-
Descrição: dc.descriptionDepartamento de Matemática IBILCE-UNESP, Rua C. Colombo, 2265-
Idioma: dc.languageen-
Relação: dc.relationDifferential Equations and Dynamical Systems-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectNon-smooth vector fields-
Palavras-chave: dc.subjectRegularization-
Palavras-chave: dc.subjectSingular perturbation-
Palavras-chave: dc.subjectSliding vector fields-
Palavras-chave: dc.subjectVector fields-
Título: dc.titleNonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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