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.
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Submitted on : Thursday, December 20, 2018 - 9:21:54 AM
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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⟩



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