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History-dependent operators and prox-regular sweeping processes. (English) Zbl 07525634

MSC:

47J22 Variational and other types of inclusions
34G25 Evolution inclusions
45G10 Other nonlinear integral equations
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
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[1] Adly, S.; Haddad, T., An implicit sweeping process approach to quasistatic evolution variational inequalities, SIAM J. Math. Anal., 50, 761-778 (2018) · Zbl 1382.49007
[2] Adly, S.; Nacry, F.; Thibault, L., Preservation of prox-regularity of sets with applications to constrained optimization, SIAM J. Optim., 26, 448-473 (2016) · Zbl 1333.49031
[3] Adly, S.; Nacry, F.; Thibault, L., Discontinuous sweeping process with prox-regular sets, ESAIM Control Optim. Calc. Var., 23, 1293-1329 (2017) · Zbl 1379.49023
[4] Adly, S.; Nacry, F.; Thibault, L., Prox-regularity approach to generalized equations and image projection, ESAIM Control Optim. Calc. Var., 24, 677-708 (2018) · Zbl 1409.49014
[5] Adly, S.; Sofonea, M., Time-dependent inclusions and sweeping processes in contact mechanics, Z. Angew. Math. Phys., 70, 2 (2019) · Zbl 1409.49008
[6] Cao, T. H.; Mordukhovich, B. S., Optimal control of a nonconvex perturbed sweeping process, J. Differ. Equ., 266, 1003-1050 (2019) · Zbl 1404.49014
[7] Castaing, C.; Ibrahim, A. G.; Yarou, M., Some contributions to nonconvex sweeping process, J. Nonlinear Convex Anal., 10, 1-20 (2009) · Zbl 1185.34017
[8] Chemetov, N.; Monteiro Marques, M. D.P., Non-convex quasi-variational differential inclusions, Set-Valued Anal., 15, 209-221 (2007) · Zbl 1134.34036
[9] Clarke, F. H., Optimization and Nonsmooth Analysis (1990), Philadelphia: SIAM, Philadelphia · Zbl 0696.49002
[10] Colombo, G.; Goncharov, V. V., The sweeping processes without convexity, Set-Valued Anal., 7, 357-374 (1999) · Zbl 0957.34060
[11] Colombo, G.; Thibault, L., Prox-regular sets and applications, Handbook of Nonconvex Analysis and Applications, 99-182 (2010), Somerville: Int. Press, Somerville · Zbl 1221.49001
[12] Edmond, J. F.; Thibault, L., BV solutions of nonconvex sweeping process differential inclusions with perturbation, J. Differ. Equ., 226, 135-179 (2006) · Zbl 1110.34038
[13] Haddad, T., Nonconvex differential variational inequality and state-dependent sweeping process, J. Optim. Theory Appl., 159, 386-398 (2013) · Zbl 1357.49034
[14] Jourani, A.; Vilches, E., Positively α-far sets and existence results for generalized perturbed sweeping processes, J. Convex Anal., 23, 775-821 (2016) · Zbl 1350.49015
[15] Monteiro Marques, M. D.P., Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and Dry Friction (1993), Basel: Birkhäuser, Basel · Zbl 0802.73003
[16] Mordukhovich, B. S., Variational Analysis and Applications (2018), Cham: Springer, Cham · Zbl 1402.49003
[17] Moreau, J. J., Rafle par un convexe variable I, Travaux Sém. Anal. Convexe Montpellier (1971) · Zbl 0343.49019
[18] Moreau, J. J., Evolution problem associated with a moving convex in a Hilbert space, J. Differ. Equ., 26, 347-374 (1977) · Zbl 0356.34067
[19] Nacry, F.; Sofonea, M., A class of nonlinear inclusions and sweeping processes in solid mechanics, Acta Appl. Math., 171 (2021) · Zbl 07363541
[20] Nacry, F., Sofonea, M.: A history-dependent sweeping processes in contact mechanics. J. Convex Anal. 29 (2022, to appear) · Zbl 1485.74072
[21] Nacry, F.; Thibault, L., Regularization of sweeping process: old and new, Pure Appl. Funct. Anal., 4, 59-117 (2019) · Zbl 1454.34038
[22] Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applications (1985), Boston: Birkhäuser, Boston · Zbl 0579.73014
[23] Poliquin, R. A.; Rockafellar, R. T.; Thibault, L., Local differentiability of distance functions, Transl. Am. Math. Soc., 352, 5231-5249 (2000) · Zbl 0960.49018
[24] Rockafellar, R. T.; Wets, R. J.-B., Variational Analysis (1997), Berlin: Springer, Berlin · Zbl 0888.49001
[25] Sofonea, M.; Matei, A., Mathematical Models in Contact Mechanics (2012), Cambridge: Cambridge University Press, Cambridge · Zbl 1255.49002
[26] Sofonea, M.; Migórski, S., Variational-Hemivariational Inequalities with Applications (2018), Boca Raton-London: Chapman & Hall/CRC Press, Boca Raton-London · Zbl 1384.49002
[27] Thibault, L., Sweeping process with regular and nonregular sets, J. Differ. Equ., 193, 1-26 (2003) · Zbl 1037.34007
[28] Thibault, L.: Unilateral variational analysis in Banach spaces (to appear) · Zbl 07502906
[29] Venel, J., A numerical scheme for a class of sweeping processes, Numer. Math., 118, 367-400 (2011) · Zbl 1222.65064
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