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All issues Volume 15 (2020) Math. Model. Nat. Phenom., 15 (2020) 13 References
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
Article Number 13
Number of page(s) 17
DOI https://doi.org/10.1051/mmnp/2019042
Published online 12 March 2020
  1. 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]
  2. R. Bouc, Modèle mathématique d’hystérésis. Acustica 24 (1971) 16–25. [Google Scholar]
  3. H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematical Studies, Vol. 5, North-Holland Publishing Company, Amsterdam (1973). [Google Scholar]
  4. M. Brokate and J. Sprekels, Hysteresis and Phase Transitions. Vol. 121 of Applied Mathematical Sciences. Springer-Verlag, New York (1996). [CrossRef] [Google Scholar]
  5. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions. Springer, Berlin - Heidelberg - New York (1977). [CrossRef] [Google Scholar]
  6. N. Dinculeanu, Vector Measures, International Series of Monographs in Pure and Applied Mathematics, Vol. 95, Pergamon Press, Berlin (1967). [Google Scholar]
  7. H. Federer, Geometric Measure Theory. Springer-Verlag, Berlin-Heidelberg (1969). [Google Scholar]
  8. O. Klein, Representation of hysteresis operators acting on vector-valued monotaffine functions. Adv. Math. Sci. Appl. 22 (2012) 471–500. [Google Scholar]
  9. O. Klein, A representation result for hysteresis operators with vector valued inputs and its application to models for magnetic materials. Physica B 435 (2014) 113–115. [CrossRef] [Google Scholar]
  10. O. Klein, On the representation of hysteresis operators acting on vector-valued, left-continuous and piecewise monotaffine and continuous functions. Discrete Contin. Dyn. Syst. 35 (2015) 2591–2614. [CrossRef] [Google Scholar]
  11. O. Klein, A representation result for rate-independent systems. Physica B 486 (2016) 81–83. [CrossRef] [Google Scholar]
  12. J. Kopfová and V. Recupero, BV-norm continuity of sweeping processes driven by a set with constant shape. J. Differ. Equ. 261 (2016) 5875–5899. [Google Scholar]
  13. M.A. Krasnosel’skiǐ and A.V. Pokrovskiǐ, Systems with Hysteresis. Springer-Verlag, Berlin Heidelberg (1989). [CrossRef] [Google Scholar]
  14. P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations. Vol. 8 of Gakuto International Series Mathematical Sciences and Applications. Gakkōtosho, Tokyo (1997). [Google Scholar]
  15. P. Krejčí and P. Laurençot, Generalized variational inequalities. J. Convex Anal. 9 (2002) 159–183. [Google Scholar]
  16. P. Krejčí and V. Recupero, Comparing BV solutions of rate independent processes. J. Convex Anal. 21 (2014) 121–146. [Google Scholar]
  17. P. Krejčí and V. Recupero, BV solutions of rate independent differential inclusions. Math. Bohem. 139 (2014) 607–619. [Google Scholar]
  18. S. Lang, Real and Functional Analysis - Third Edition. Springer Verlag, New York (1993). [CrossRef] [Google Scholar]
  19. A. Mielke and T. Roubíček, Rate Independent Systems, Theory and Applications. Springer (2015). [CrossRef] [Google Scholar]
  20. M.D.P. Monteiro Marques, Differential Inclusions in Nonsmooth Mechanical Problems - Shocks and Dry Friction. Birkhauser Verlag, Basel (1993). [CrossRef] [Google Scholar]
  21. J.J. Moreau, Rafle par un convexe variable, I. Sem. d’Anal. Convexe, Montpellier, Exposé No. 15, Vol. 1 (1971). [Google Scholar]
  22. J.J. Moreau, Sur les mesures différentielles de fonctions vectorielles et certains problémes d’évolution. C. R. Math. Acad. Sci. Paris Sér. A 282 (1976) 837–840. [Google Scholar]
  23. J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space. J. Differ. Equ. 26 (1977) 347–374. [Google Scholar]
  24. V. Recupero, The play operator on the rectifiable curves in a Hilbert space. Math. Methods Appl. Sci. 31 (2008) 1283–1295. [Google Scholar]
  25. V. Recupero, BV solutions of rate independent variational inequalities. Ann. Sc. Norm. Super. Pisa Cl. Sc. 10 (2011) 269–315. [Google Scholar]
  26. V. Recupero, A continuity method for sweeping processes. J. Differ. Equ. 251 (2011) 2125–2142. [Google Scholar]
  27. V. Recupero, Sweeping processes and rate independence. J. Convex Anal. 23 (2016) 921–946. [Google Scholar]
  28. V. Recupero and F. Santambrogio, Sweeping processes with prescribed behavior on jumps. Ann. Mat. Pura Appl. 197 (2018) 1311–1332. [Google Scholar]
  29. J. Serra, Hausdorff distances and interpolations. ISMM ’98 Proceedings of the fourth symposium on Mathematical morphology and its applications to image and signal processing, edited by H. Heijmans and J. Roerdink. Kluwer Acad. Publ. (1998) 107–114. [Google Scholar]
  30. A. Visintin, Differential Models of Hysteresis. In Vol. 111 of Applied Mathematical Sciences. Springer-Verlag, Berlin Heidelberg (1994). [Google Scholar]

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