Galerkin-like method and generalized perturbed sweeping process with nonregular sets

Abderrahim Jourani; Emilio Vilches

Galerkin-like method and generalized perturbed sweeping process with nonregular sets

Abderrahim Jourani ^{1, *} Emilio Vilches ²

* Auteur correspondant

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

2 DIM - Departamento de Ingeniería Matemática [Santiago]

Abstract : In this paper we present a new method to solve differential inclusions in Hilbert spaces. This method is a Galerkin-like method where we approach the original problem by projecting the state into a $n$-dimensional Hilbert space but not the velocity. We prove that the approached problem always has a solution and that, under some compactness conditions, the approached problems have a subsequence which converges strongly pointwisely to a solution of the original differential inclusion. We apply this method to the generalized perturbed sweeping process governed by nonregular sets (equi-uniformly subsmooth or positively $\alpha$-far). This differential inclusion includes Moreau's sweeping process, the state-dependent sweeping process, and second-order sweeping process for which we give very general existence results.

Keywords : Sweeping process Subsmooth sets Positively α -far sets Differential inclusions Second-order sweeping process Normal cone

Type de document :

Article dans une revue

Domaine :

Mathématiques [math]

Liste complète des métadonnées

https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01611933
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 6 octobre 2017 - 13:04:42
Dernière modification le : mercredi 13 février 2019 - 18:30:03

Galerkin-like method and generalized perturbed sweeping process with nonregular sets

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Galerkin-like method and generalized perturbed sweeping process with nonregular sets

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