Previous |  Up |  Next

Article

Title: On noncompact perturbation of nonconvex sweeping process (English)
Author: Aitalioubrahim, Myelkebir
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 53
Issue: 1
Year: 2012
Pages: 65-77
Summary lang: English
.
Category: math
.
Summary: We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation. (English)
Keyword: nonconvex sweeping process
Keyword: functional differential inclusion
Keyword: uniformly $\rho$-prox-regular sets
MSC: 34A60
MSC: 34B15
MSC: 47H10
idZBL: Zbl 1249.34183
idMR: MR2880911
.
Date available: 2012-02-07T10:24:20Z
Last updated: 2014-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/141826
.
Reference: [1] Aubin J.P., Cellina A.: Differential Inclusions.Springer, Berlin-Heidelberg, 1984. Zbl 0538.34007, MR 0755330
Reference: [2] Bounkhel M., Thibault L.: Nonconvex sweeping process and prox-regularity in Hilbert space.J. Nonlinear Convex Anal. 6 (2005), no. 2, 359–374. Zbl 1086.49016, MR 2159846
Reference: [3] Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Mathematics, 580, Springer, Berlin-Heidelberg-New York, 1977. Zbl 0346.46038, MR 0467310, 10.1007/BFb0087688
Reference: [4] Castaing P., Monteiro Marques M.D.P.: Topological properties of solution sets for sweeping process with delay.Portugal. Math. 54 (1997), 485–507. MR 1489988
Reference: [5] Clarke F.H., Stern R.J., Wolenski P.R.: Proximal smoothness and the lower $C^2$ property.J. Convex Anal. 2 (1995), no. 1–2, 117–144. MR 1363364
Reference: [6] Edmond J.F.: Delay perturbed sweeping process.Set-Valued Anal. 14 (2006), no. 3, 295-317. Zbl 1122.34060, MR 2252653, 10.1007/s11228-006-0021-9
Reference: [7] Edmond J.F., Thibault L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation.J. Differential Equations 226 (2006), 135–179. Zbl 1110.34038, MR 2232433, 10.1016/j.jde.2005.12.005
Reference: [8] Haddad T., Thibault L.: Mixed semicontinuous perturbations of nonconvex sweeping process.Math. Program. 123 (2010), no. 1, Ser. B, 225–240. MR 2577329, 10.1007/s10107-009-0315-4
Reference: [9] Moreau J.J.: Evolution problem associated with a moving convex set in a Hilbert space.J. Differential Equations 26 (1977), 347–374. Zbl 0351.34038, MR 0508661, 10.1016/0022-0396(77)90085-7
Reference: [10] Moreau J.J.: Application of convex analysis to the treatment of elasto-plastic systems.in Applications of Methods of Functional Analysis to Problems in Mechanics (Germain and Nayroles, Eds.), Lecture Notes in Mathematics, 503, Springer, Berlin, 1976, pp. 56–89.
Reference: [11] Moreau J.J.: Unilateral contact and dry friction in finite freedom dynamics.in Nonsmooth Mechanics (J.J. Moreau and P.D. Panagiotopoulos, Eds.), CISM Courses and Lectures, 302, Springer, Vienna-New York, 1988, pp. 1–82. Zbl 0703.73070
Reference: [12] Poliquin R.A., Rockafellar R.T., Thibault L.: Local differentiability of distance functions.Trans. Amer. Math. Soc. 352 (2000), no. 11, 5231–5249. Zbl 0960.49018, MR 1694378, 10.1090/S0002-9947-00-02550-2
Reference: [13] Thibault L.: Sweeping process with regular and nonregular sets.J. Differential Equations 193 (2003), 1–23. Zbl 1037.34007, MR 1994056, 10.1016/S0022-0396(03)00129-3
Reference: [14] Valadier M., Duc Ha T.X., Castaing C.: Evolution equations governed by the sweeping process.Set Valued Anal. 1 (1993), 109–139. Zbl 0813.34018, MR 1239400
Reference: [15] Zhu Q.: On the solution set of differential inclusions in Banach space.J. Differential Equations 93 (1991), 213–237. Zbl 0735.34017, MR 1125218, 10.1016/0022-0396(91)90011-W
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_53-2012-1_5.pdf 484.2Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo