Perturbed sweeping process with a subsmooth set depending on the state

Tahar Haddad (1) , Lionel Thibault (2) , Jimmy Noel

1 UMSBJ - Université Mohammed Seddik Benyahia [Jijel] | University of Jijel
2 IMAG - Institut Montpelliérain Alexander Grothendieck

The class of subsmooth sets introduced in strictly contains the class of closed convex sets and the class of prox-regular sets. The present paper is concerned with the study of perturbed differential sweeping process inclusions where the moving set is nonconvex and non prox-regular and depends both on the time and on the state. We prove the existence of solution under the subsmoothness of the moving set.

Mots clés: Prox-regular set; Normal cone; Sweeping process; Differential inclusion; Subsmooth sets

Domaines: Mathématiques [math]

Tahar Haddad, Lionel Thibault, Jimmy Noel. Perturbed sweeping process with a subsmooth set depending on the state. Linear and Nonlinear Analysis, 2016, 2 (1), pp.155-174. ⟨hal-02072778⟩