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
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.2412 - 2436. 〈10.1137/16M1078288〉
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 : mardi 27 mars 2018 - 14:03:58

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Abderrahim Jourani, Emilio Vilches. Galerkin-like method and generalized perturbed sweeping process with nonregular sets. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.2412 - 2436. 〈10.1137/16M1078288〉. 〈hal-01611933〉

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