Geodesic
Second order state-dependent sweeping process with unbounded perturbation
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2021), pp. 50-71

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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. 
@article{BASM_2021_3_a5,
     author = {Doria Affane and Nora Fetouci and Mustapha Fateh Yarou},
     title = {Second order state-dependent sweeping process with unbounded perturbation},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {50--71},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2021_3_a5/}
}
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Doria Affane; Nora Fetouci; Mustapha Fateh Yarou. Second order state-dependent sweeping process with unbounded perturbation. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2021), pp. 50-71. http://geodesic.mathdoc.fr/item/BASM_2021_3_a5/