References
- Vladimirov AA. Nonstationary dissipative evolution equations in a Hilbert space. Nonlinear Anal. 1991;17:499–518. doi: https://doi.org/10.1016/0362-546X(91)90061-5
- Azzam-Laouir D, Belhoula W, Castaing C, et al. Perturbed evolution problems with absolutely continuous variation in time and applications. J Fixed Point Theory Appl. 2019;21(2). art. 40. doi: https://doi.org/10.1007/s11784-019-0666-2
- Azzam-Laouir D, Belhoula W, Castaing C, et al. Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators. Evol Equ Control Theory. 2020;9(1):219–254. doi: https://doi.org/10.3934/eect.2020004
- Azzam-Laouir D, Boutana-Harid I. Mixed semicontinuous perturbation to an evolution problem with time-dependent maximal monotone operator. J Nonlinear Convex Anal. 2019;20(1):39–52.
- Azzam-Laouir D, Castaing C, Monteiro Marques MDP. Perturbed evolution problems with continuous bounded variation in time and applications. Set-Valued Var Anal. 2018;26(3):693–728. doi: https://doi.org/10.1007/s11228-017-0432-9
- Kenmochi N. Solvability of nonlinear evolution equations with time-dependent constraints and applications. Bull Fac Educ Chiba Univ. 1981;30:1–81.
- Kunze M, Monteiro Marques MDP. BV solutions to evolution problems with time-dependent domains. Set-Valued Anal. 1997;5:57–72. doi: https://doi.org/10.1023/A:1008621327851
- Pavel NH. Nonlinear evolution operators and semigroups. Vol. 1260. Lecture Notes in Mathematics. New York (NY): Springer; 1987.
- Le BK. Well-posedeness and nonsmooth Lyapunov pairs for state-dependent maximal monotone differential inclusions. Optimization. 2019. Available from: https://doi.org/https://doi.org/10.1080/02331934.2019.1686504.
- Barbu V. Nonlinear semigroups and differential equations in Banach spaces. Leyden: Noordhoff Int Publ.; 1976.
- Brezis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Amsterdam, London: North-Holland; 1973.
- Vrabie II. Compactness methods for nonlinear evolutions, Pitman Monographs and Surveys in Pure and Applied Mathematics. Vol. 32. Longman Scientific and Technical. New York (NY): John Wiley and Sons; 1987.
- Moreau JJ. Evolution problem associated with a moving convex set in a Hilbert space. J Differ Equ. 1977;26:347–374. doi: https://doi.org/10.1016/0022-0396(77)90085-7
- Monteiro Marques MDP. Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction. Progress in Nonlinear Differential Equations and Their Applications. Vol. 9. Birkhäuser; 1993.
- Thibault L. Sweeping process with regular and nonregular sets. J Differ Equ. 2003;193:1–26. doi: https://doi.org/10.1016/S0022-0396(03)00129-3
- Valadier M. Quelques résultats de base concernant le processus de rafle. Sém Anal Convexe Montpellier, Vol 18 (1988) exposé 3.
- Azzam-Laouir D, Selamnia F. On state-dependent sweeping process in Banach spaces. Evol Equ Control Theory. 2018;7(2):183–196. doi: https://doi.org/10.3934/eect.2018009
- Chemetov NV, Monteiro Marques MDP. Non-convex quasi-variational differential inclusions. Set-Valued Anal. 2007;1:209–221. doi: https://doi.org/10.1007/s11228-007-0045-9
- Chemetov NV, Monteiro Marques MDP, Stefanelli U. Ordered non-convex quasi-variational sweeping process. J Convex Anal. 2008;15(2):201–214.
- Jourani A, Vilches E. Moreau-Yosida regularization of state-dependent sweeping processes with nonregular sets. J Optim Theory Appl. doi:https://doi.org/10.1007/s10957-017-1083-6.
- Kunze M, Monteiro Marques MDP. On parabolic quasi-variational inequalities and state-dependent sweeping processes. Topol Methods Nonlinear Anal. 1998;12:179–191. doi: https://doi.org/10.12775/TMNA.1998.036
- Kunze M, Monteiro Marques MDP. An introduction to Moreau's sweeping process, In: Brogliato B, editor. Impacts in mechanical systems. Analysis and modelling. Berlin: Springer: 2000. p. 1–60.
- Noel J, Thibault L. Nonconvex sweeping process with a moving set depending on the state. Vietnam J Math. 2014;42:595–612. doi: https://doi.org/10.1007/s10013-014-0109-8
- Azzam-Laouir D, Makhlouf M, Thibault L. On perturbed sweeping process. Appl Anal. 2016;95(2):303–322. doi: https://doi.org/10.1080/00036811.2014.1002482
- Nacry F. Perturbed BV sweeping process involving prox-regular sets. J Nonlinear Convex Anal. 2017;18:1619–1651.