Existence and Lyapunov Pairs for the Perturbed Sweeping Process Governed by a Fixed Set

Emilio Vilches (1, 2, 3)

1 DIM - Departamento de Ingeniería Matemática [Santiago]
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 ICEd - UOH - Instituto de Ciencias de la educacion

The aim of this paper is to prove existence results for a class of sweeping processes in Hilbert spaces by using the catching-up algorithm. These processes are governed by ball-compact non autonomous sets. Moreover, a full characterization of nonsmooth Lyapunov pairs is obtained under very general hypotheses. We also provide a criterion for weak invariance. Some applications to hysteresis and crowd motion are given.

Mots clés: Sweeping process; Lyapunov pair; Differential inclusions; Invariance; Normal cone

Domaines: Mathématiques [math]

Emilio Vilches. Existence and Lyapunov Pairs for the Perturbed Sweeping Process Governed by a Fixed Set. Set-Valued and Variational Analysis, 2019, 27 (2), pp.569-583. ⟨10.1007/s11228-018-0480-9⟩. ⟨hal-02194585⟩