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Article Dans Une Revue Fixed Point Theory and Algorithms for Sciences and Engineering Année : 2022

History-dependent operators and prox-regular sweeping processes

Résumé

Abstract We consider an abstract inclusion in a real Hilbert space, governed by an almost history-dependent operator and a time-dependent multimapping with prox-regular values. We establish the unique solvability of the inclusion under appropriate assumptions on the data. The proof is based on the arguments of monotonicity, fixed point, and prox-regularity. We then use our result in order to deduce some direct consequences, including an existence and uniqueness result for a class of sweeping processes associated with prox-regular sets. Finally, we provide an example in a finite dimensional case inspired by a rheological model in solid mechanics.

Dates et versions

hal-04193918 , version 1 (01-09-2023)

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Florent Nacry, Mircea Sofonea. History-dependent operators and prox-regular sweeping processes. Fixed Point Theory and Algorithms for Sciences and Engineering, 2022, 2022 (1), pp.5. ⟨10.1186/s13663-022-00715-w⟩. ⟨hal-04193918⟩

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