Affane, Doria; Yarou, Mustapha Fateh Second-order perturbed state-dependent sweeping process with subsmooth sets. (English) Zbl 1486.34057 Zeidan, Dia (ed.) et al., Computational mathematics and applications. Singapore: Springer. Forum Interdiscip. Math., 147-169 (2020). Summary: Using a discretisation approach, the existence of solutions for a class of second-order differential inclusion is stated. The right-hand side of the problem is governed by the so-called nonconvex state-dependent sweeping process and contains an unbounded perturbation, that is the external forces applied on the system. Thanks to some recent concepts of set’s regularity and nonsmooth analysis, we extend existence results for nonconvex equi-uniformly subsmooth sets. The construction is based on Moreau’s catching-up algorithm. Moreover, we extend our result to the more general delayed case, namely when the perturbation contains a finite delay. An example is given for the special case of quasi-variational inequalities which constitutes a variational formulation of certain linear elasticity problems with friction or unilateral constraints.For the entire collection see [Zbl 1464.65006]. Cited in 2 Documents MSC: 34A60 Ordinary differential inclusions 49J40 Variational inequalities 49J52 Nonsmooth analysis 65K99 Numerical methods for mathematical programming, optimization and variational techniques PDFBibTeX XMLCite \textit{D. Affane} and \textit{M. F. Yarou}, in: Computational mathematics and applications. Singapore: Springer. 147--169 (2020; Zbl 1486.34057) Full Text: DOI References: [1] Adly, S., Haddad, T., Le, B.K.: State-dependent implicit sweeping process in the framework of quasistatic evolution quasi-variational inequalities. J. Optim. Theory Appl. 182(2), 473-493 (2019) · Zbl 1421.49008 [2] Affane, D., Yarou, M. F.: Unbounded perturbation for a class of variational inequalities. Discuss. Math. Diff. 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