Journal of Convex Analysis 31 (2024), No. 4, 1057--1138
Copyright Heldermann Verlag 2024
Evolution Inclusions with and without Rough Signals
Charles Castaing
Inst. Montpelliérain A. Grothendieck, Université de Montpellier, Montpellier, France
charles.castaing@gmail.com
Christiane Godet-Thobie
Lab. de Mathématiques de Bretagne Atlantique, Université de Brest, Brest, France
christiane.godet-thobie@univ-brest.fr
Manuel D. P. Monteiro Marques
Departemento de Matematica, Faculdade de Ciencias, Lisboa, Portugal
mdmarques@fc.ul.pt
Lionel Thibault
Inst. Montpelliérain A. Grothendieck, Université de Montpellier, France
lionel.thibault@umontpellier.fr
The paper studies diverse differential evolution inclusions involving rough signals and governed by time-dependent maximal monotone operators or subdifferentials evaluated at the velocity or the state. Their coupling with fractional order differential equations as well as their corresponding sweeping processes are also considered.
Keywords: Sweeping process, maximal monotone operator, rough signal, fractional differential inclusion, prox-regular set, Volterra-type integral.
MSC: 34A60, 49I52, 49J53.
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