Second order state-dependent sweeping process with unbounded perturbation
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517.9 (242)
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (240)
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AFFANE, Doria, FETOUCI, Nora, YAROU, Mustapha Fateh. Second order state-dependent sweeping process with unbounded perturbation. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2021, nr. 3(97), pp. 50-71. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 3(97) / 2021 / ISSN 1024-7696 /ISSNe 2587-4322

Second order state-dependent sweeping process with unbounded perturbation

CZU: 517.9
MSC 2010: 34A60, 49J53 .

Pag. 50-71

Affane Doria, Fetouci Nora, Yarou Mustapha Fateh
 
University of Jijel
 
Disponibil în IBN: 13 octombrie 2022


Rezumat

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 Carath´eodory 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.

Cuvinte-cheie
Differential inclusion, uniformly prox-regular sets, unbounded perturbation, Carath´eodory mapping, delay