On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 65-77
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

Aitalioubrahim, Myelkebir. "On noncompact perturbation of nonconvex sweeping process." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 65-77. <http://eudml.org/doc/246397>.

@article{Aitalioubrahim2012,
abstract = {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.},
author = {Aitalioubrahim, Myelkebir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonconvex sweeping process; functional differential inclusion; uniformly $\rho $-prox-regular sets; nonconvex sweeping process; functional differential inclusion; existence result},
language = {eng},
number = {1},
pages = {65-77},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On noncompact perturbation of nonconvex sweeping process},
url = {http://eudml.org/doc/246397},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Aitalioubrahim, Myelkebir
TI - On noncompact perturbation of nonconvex sweeping process
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 65
EP - 77
AB - 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.
LA - eng
KW - nonconvex sweeping process; functional differential inclusion; uniformly $\rho $-prox-regular sets; nonconvex sweeping process; functional differential inclusion; existence result
UR - http://eudml.org/doc/246397
ER -

References

top
  1. Aubin J.P., Cellina A., Differential Inclusions, Springer, Berlin-Heidelberg, 1984. Zbl0538.34007MR0755330
  2. Bounkhel M., Thibault L., Nonconvex sweeping process and prox-regularity in Hilbert space, J. Nonlinear Convex Anal. 6 (2005), no. 2, 359–374. Zbl1086.49016MR2159846
  3. Castaing C., Valadier M., 10.1007/BFb0087688, Lecture Notes in Mathematics, 580, Springer, Berlin-Heidelberg-New York, 1977. Zbl0346.46038MR0467310DOI10.1007/BFb0087688
  4. Castaing P., Monteiro Marques M.D.P., Topological properties of solution sets for sweeping process with delay, Portugal. Math. 54 (1997), 485–507. MR1489988
  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. MR1363364
  6. Edmond J.F., 10.1007/s11228-006-0021-9, Set-Valued Anal. 14 (2006), no. 3, 295-317. Zbl1122.34060MR2252653DOI10.1007/s11228-006-0021-9
  7. Edmond J.F., Thibault L., 10.1016/j.jde.2005.12.005, J. Differential Equations 226 (2006), 135–179. Zbl1110.34038MR2232433DOI10.1016/j.jde.2005.12.005
  8. Haddad T., Thibault L., 10.1007/s10107-009-0315-4, Math. Program. 123 (2010), no. 1, Ser. B, 225–240. MR2577329DOI10.1007/s10107-009-0315-4
  9. Moreau J.J., 10.1016/0022-0396(77)90085-7, J. Differential Equations 26 (1977), 347–374. Zbl0351.34038MR0508661DOI10.1016/0022-0396(77)90085-7
  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. 
  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. Zbl0703.73070
  12. Poliquin R.A., Rockafellar R.T., Thibault L., 10.1090/S0002-9947-00-02550-2, Trans. Amer. Math. Soc. 352 (2000), no. 11, 5231–5249. Zbl0960.49018MR1694378DOI10.1090/S0002-9947-00-02550-2
  13. Thibault L., 10.1016/S0022-0396(03)00129-3, J. Differential Equations 193 (2003), 1–23. Zbl1037.34007MR1994056DOI10.1016/S0022-0396(03)00129-3
  14. Valadier M., Duc Ha T.X., Castaing C., Evolution equations governed by the sweeping process, Set Valued Anal. 1 (1993), 109–139. Zbl0813.34018MR1239400
  15. Zhu Q., 10.1016/0022-0396(91)90011-W, J. Differential Equations 93 (1991), 213–237. Zbl0735.34017MR1125218DOI10.1016/0022-0396(91)90011-W

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.