Second order state-dependent sweeping process with unbounded perturbation

Doria Affane ; Nora Fetouci ; Mustapha Fateh Yarou

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2021), pp. 50-71.

Résumé

We establish, in the setting of an infinite dimensional Hilbert space, results concerning the existence of solutions of second order "nonconvex sweeping process" for a class of uniformly prox-regular sets depending on time and state. The perturbation considered here is general and takes the form of a sum of a single-valued Carathéodory mapping and a set-valued unbounded mapping. We deal also with a delayed perturbation, that is the external forces applied on the system in presence of a finite delay. We extend a discretization approach known for the time-dependent case to the time and state-dependent sweeping process.

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