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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2017

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

Abderrahim Jourani

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Emilio Vilches

#### Résumé

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.

#### Domaines

Mathématiques [math]

### Dates et versions

hal-01611933 , version 1 (06-10-2017)

### Identifiants

• HAL Id : hal-01611933 , version 1
• DOI :

### Citer

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

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