6533b85cfe1ef96bd12bc8f9

RESEARCH PRODUCT

A differential equation approach to implicit sweeping processes

Abderrahim JouraniEmilio Vilches

subject

Lyapunov functionDifferential equation01 natural scienceslaw.inventionsymbols.namesakeEvolution variational inequalitylawApplied mathematicsUniqueness0101 mathematicsEquivalence (formal languages)[MATH]Mathematics [math]MathematicsConvex analysisApplied Mathematics010102 general mathematicsNonsmooth Lyapunov pairs010101 applied mathematicsregularizationMSC: 49J40 47J20 47J22 34G25 58E35 37L45Electrical networkVariational inequalitysymbolsMoreau's sweeping processAnalysisQuasistatic process

description

International audience; 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.

yearjournalcountryeditionlanguage
2019-04-05
10.1016/j.jde.2018.10.024https://hal.archives-ouvertes.fr/hal-01961594