A differential equation approach to implicit sweeping processes

Abstract : In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01961594
Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, December 20, 2018 - 9:21:54 AM
Last modification on : Thursday, June 27, 2019 - 11:47:20 AM

Identifiers

Collections

Citation

Abderrahim Jourani, Emilio Vilches. A differential equation approach to implicit sweeping processes. Journal of Differential Equations, Elsevier, 2019, 266 (8), pp.5168-5184. ⟨https://www-sciencedirect-com.proxy-scd.u-bourgogne.fr/science/article/pii/S0022039618306120⟩. ⟨10.1016/j.jde.2018.10.024⟩. ⟨hal-01961594⟩

Share

Metrics

Record views

41