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Non-convex Quasi-variational Differential Inclusions

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Abstract

In this article we discuss the evolution problem known as sweeping process for a class of prox-regular non-convex sets. Assuming that such sets depend continuously on time and state, we prove local and global existence of solutions which are absolutely continuous functions.

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References

  1. Benabdellah, H., Castaing, C., Salvadori, A., Syam, A.: Nonconvex sweeping process. J. Appl. Anal. 2, 217–240 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Benabdellah, H.: Existence of solutions to the nonconvex sweeping process. J. Differential Equations 164, 286–295 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Benabdellah, H.: Differential inclusions on closed sets in Banach spaces with application to sweeping process. Topol. Methods Nonlinear Anal. 23, 115–148 (2004)

    MATH  MathSciNet  Google Scholar 

  4. Canino, A.: Local properties of geodesics on p-convex sets. Ann. Mat. Pura Appl. 159, 17–44 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Castaing, C.: Équation différentielle multivoque avec contrainte sur l’état dans les espaces de Banach, In: Sém. Anal. Convexe, Montpellier, Exp. 13 (1978)

  6. Colombo, G., Goncharov, V.V.: The sweeping processes without convexity. Set-Valued Anal. 7, 357–374 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Colombo, G., Goncharov, V.V.: Variational inequalities and regularity properties of closed sets in Hilbert spaces. J. Convex Anal. 8, 197–221 (2001)

    MATH  MathSciNet  Google Scholar 

  8. Colombo, G., Monteiro Marques, M.D.P.: Sweeping by a continuous prox-regular set. J. Differential Equations 187, 46–62 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Edmond, J.F., Thibault, L.: BV solutions of nonconvex sweeping process differential inclusion with perturbation. J. Differential Equations 226, 135–179 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kunze, M., Monteiro Marques, M.D.P.: On parabolic quasi-variational inequalities and state-dependent sweeping processes. Topol. Methods Nonlinear Anal. 12, 179–191 (1998)

    MATH  MathSciNet  Google Scholar 

  11. Monteiro Marques, M.D.P.: Differential Inclusions in Nonsmooth Mechanical Problems. Birkhäuser, Basel (1993)

    MATH  Google Scholar 

  12. Moreau, J.J.: Rafle par um convexe variable, 1ere partie, In: Sém. d’Analyse Convexe, Montpellier, Exp. 15 (1971)

  13. Moreau, J.J.: Evolution problem associated with a moving convex set in a Hilbert space. J. Differential Equations 26, 347–374 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  14. Rossi, R., Stefanelli, U.: An order approach to a class of quasivariational sweeping processes. Adv. Differential Equations 10, 527–552 (2005)

    MATH  MathSciNet  Google Scholar 

  15. Thibault, L.: Sweeping process with regular and nonregular sets. J. Differential Equations 193, 1–26 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Valadier, M.: Quelques résultats de base concernant le processus de rafle, In: Sém. Anal. Convexe, Montpellier, Exp. 3 (1988)

  17. Valadier, M.: Quelques problèmes d’entraînement unilatéral de dimension finie, In: Sém. Anal. Convexe, Montpellier, Exp. 8 (1988)

  18. Valadier, M.: Rafle et viabilité, In: Sém. Anal. Convexe, Montpellier, Exp. 17 (1992)

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Authors and Affiliations

  1. Centro de Matemática e Aplicações Fundamentais, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    N. Chemetov & M. D. P. Monteiro Marques

  2. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Edifício C6, Campo Grande, 1749-016, Lisboa, Portugal

    N. Chemetov & M. D. P. Monteiro Marques

Authors
  1. N. Chemetov
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  2. M. D. P. Monteiro Marques
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Correspondence to N. Chemetov.

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Chemetov, N., Monteiro Marques, M.D.P. Non-convex Quasi-variational Differential Inclusions. Set-Valued Anal 15, 209–221 (2007). https://doi.org/10.1007/s11228-007-0045-9

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  • DOI: https://doi.org/10.1007/s11228-007-0045-9

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