Free Access
Issue |
ESAIM: COCV
Volume 23, Number 4, October-December 2017
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Page(s) | 1293 - 1329 | |
DOI | https://doi.org/10.1051/cocv/2016053 | |
Published online | 31 May 2017 |
- S. Adly, T. Haddad and L. Thibault, Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities. Math. Program. Ser. B 148 (2014) 5–47. [CrossRef] [Google Scholar]
- H. Benabdellah, Existence of solutions to the nonconvex sweeping process. J. Differ. Eqs. 164 (2000) 286–295. [CrossRef] [Google Scholar]
- M. Bounkhel, L. Thibault, On various notions of regularity of sets in nonsmooth analysis. Nonlinear Anal. Ser. A: Theory Methods 48 (2002) 223–246. [CrossRef] [Google Scholar]
- M. Bounkhel and L. Thibault, Nonconvex sweeping process and prox-regularity in Hilbert space. J. Nonlinear Convex Anal. 6 (2005) 359–374. [MathSciNet] [Google Scholar]
- C. Castaing, Equation différentielle multivoque avec contrainte sur l’état dans les espaces de Banach. Travaux Sém. Anal. Convexe. Montpellier (1978) Exposé 13. [Google Scholar]
- C. Castaing and M.D.P. Monteiro Marques, BV periodic solutions of an evolution problem associated with continuous moving convex sets. Set-Valued Anal. 3 (1995) 381–399. [CrossRef] [MathSciNet] [Google Scholar]
- C. Castaing, M.D.P. Monteiro Marques, Evolution problems associated with non-convex closed moving sets with bounded variation. Portugal. Math. 53 (1996) 73–87. [MathSciNet] [Google Scholar]
- F.H. Clarke, Functional Analysis, Calculus of Variations and Optimal Control. Springer, London (2013). [Google Scholar]
- G. Colombo and V.V. Goncharov, The sweeping processes without convexity. Set-Valued Anal. 7 (1999) 357–374. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cornet, Existence of slow solutions for a class of differential inclusions. J. Math. Anal. Appl. 96 (1983) 130–147. [Google Scholar]
- N. Dinculeanu, Vector Measures, Pergamon, Oxford (1967). [Google Scholar]
- J.F. Edmond and L. Thibault, BV solutions of nonconvex sweeping process differential inclusions with perturbation. J. Differ. Eqs. 226 (2006) 135–179. [CrossRef] [Google Scholar]
- M. Falcone, P. Saint-Pierre, Slow and quasi-slow solutions of differential inclusions. Nonlinear Anal. 11 (1987) 367–377. [CrossRef] [MathSciNet] [Google Scholar]
- H. Federer, Curvature measures. Trans. Amer. Math. Soc. 93 (1959) 418–491. [CrossRef] [MathSciNet] [Google Scholar]
- C. Henry, An existence theorem for a class of differential equations with multivalued right-hand side. J. Math. Anal. Appl. 41 (1973) 179–186. [Google Scholar]
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Cambridge Univ. Press, London (1995). [Google Scholar]
- M.D.P. Monteiro Marques, Perturbations convexes semi-continues supérieurement de problèmes d’évolution dans les espaces de Hilbert. Travaux Sém. Anal. Convexe. Montpellier (1984) Exposé 2. [Google Scholar]
- B. Maury and J. Venel, A mathematical framework for a crowd motion model, C. R. Math. Acad. Sci. Paris 346 (2008) 1245–1250. [CrossRef] [MathSciNet] [Google Scholar]
- B.S. Mordukhovich, Variational Analysis and Generalized Differentiation I. Vol. 330 Grundlehren Series. Springer (2006). [Google Scholar]
- J.J. Moreau, Rafle par un convexe variable I. Travaux Sém. Anal. Convexe. Montpellier (1971) Exposé 15. [Google Scholar]
- J.J. Moreau, On unilateral constraints, friction and plasticity. New Variational Techniques in Mathematical Physics (C.I.M.E., II Ciclo 1973). Edizioni Cremonese, Rome (1974) 171–322. [Google Scholar]
- J.J. Moreau, Sur les mesures différentielles des fonctions vectorielles à variation bornée. Travaux Sém. Anal. Convexe. Montpellier (1975) Exposé 17. [Google Scholar]
- J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space. J. Differ. Eqs. 26 (1977) 347–374. [CrossRef] [Google Scholar]
- J.J. Moreau, Bounded variation in time. Topics in nonsmooth mechanics, Vol. 174. Birkhäuser, Basel (1988). [Google Scholar]
- J.J. Moreau, Numerical aspects of the sweeping process. Comput. Methods Appl. Mech. Engrg. 177 (1999) 329–349. [CrossRef] [MathSciNet] [Google Scholar]
- J.J. Moreau, An introduction to unilateral dynamics. Novel Approaches in Civil Engineering. Edited by M. Frémond and F. Maceri. Springer, Berlin (2002). [Google Scholar]
- J.J. Moreau and M. Valadier, A chain rule involving vector functions of bounded variation. J. Funct. Anal. 74 (1987) 333–345. [Google Scholar]
- R.A. Poliquin, R.T. Rockafellar, L. Thibault, Local differentiability of distance functions. Trans. Amer. Math. Soc. 352 (2000) 5231–5249. [CrossRef] [MathSciNet] [Google Scholar]
- R.T. Rockafellar and R.J.-B. Wets, Variational Analysis. Grundlehren der Mathematischen Wissenschaften, vol. 317. Springer, New York (1998). [Google Scholar]
- A. Tanwani, B. Brogliato and C. Prieur, Stability and observer design for Lur’e systems with multivalued, nonmonotone, time-varying nonlinearities and state jumps. SIAM J. Control Optim. 52 (2014) 3639–3672. [Google Scholar]
- L. Thibault, Sweeping process with regular and nonregular sets. J. Differ. Eqs. 193 (2003) 1–26. [CrossRef] [Google Scholar]
- M. Valadier, Quelques problèmes d’entraînement unilatéral en dimension finie, Travaux Sém. Anal. Convexe. Montpellier (1988) Expos8é. [Google Scholar]
- M. Valadier, Rafle et viabilité. Travaux Sém. Anal. Convexe. Montpellier (1992) Exposé 17. [Google Scholar]
- J. Venel, A numerical scheme for a class of sweeping processes. Numer. Math. 118 (2011) 367–400. [Google Scholar]
- J.-P. Vial, Strong and weak convexity of sets and functions. Math. Oper. Res. 8 (1983) 231–259. [CrossRef] [MathSciNet] [Google Scholar]
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