Geodesic
Quasilinear hyperbolic equations with hysteresis
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 235-247.

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Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation $(\partial ^{2} / \partial t^{2}) \left[ u + \mathcal{F} (u) \right] + A u = f$; here $\mathcal{F}$ is a (possibly discontinuous) hysteresis operator, $A$ is a second order elliptic operator, $f$ is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined. 
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Visintin, Augusto. Quasilinear hyperbolic equations with hysteresis. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 235-247. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a6/

[1] G. Bertotti, Hysteresis in Magnetism. Academic Press, Boston 1998.

[2] R. Bouc, Solution périodique de l’équation de la ferrorésonance avec hystérésis. C.R. Acad. Sci. Paris, Série A, 263, 1966, 497-499. | MR | Zbl

[3] M. Brokate Et Al., Phase Transitions and Hysteresis. Lecture Notes in Mathematics, vol. 1584 (A. Visintin, ed.). Springer-Verlag, Berlin 1994. | DOI | MR | Zbl

[4] M. Brokate - J. Sprekels, Hysteresis and Phase Transitions. Springer, Berlin 1996. | DOI | MR | Zbl

[5] A. Damlamian - A. Visintin, Une généralisation vectorielle du modèle de Preisach pour l’hystérésis. C.R. Ac. Sci. Paris I, 297, 1983, 437-440. | MR | Zbl

[6] P. Duhem, The evolution of mechanics. Sijthoff and Noordhoff, Alphen aan den Rijn, 1980. Original edition: L’évolution de la méchanique. Joanin, Paris 1903. | Zbl

[7] A.Y. Ishlinskĭ, Some applications of statistical methods to describing deformations of bodies. Izv. Akad. Nauk S.S.S.R., Techn. Ser., 9, 1944, 580-590 (in Russian).

[8] M.A. Krasnosel'Skiĭ - A.V. Pokrovskiĭ, Systems with Hysteresis. Springer, Berlin 1989 (Russian ed. Nauka, Moscow 1983). | DOI | MR

[9] P. Krejčí, Convexity, Hysteresis and Dissipation in Hyperbolic Equations. Gakkotosho, Tokyo 1997. | Zbl

[10] I.D. Mayergoyz, Vector Preisach model of hysteresis. J. Appl. Phys., 63, 1988, 2995-3000. | Zbl

[11] I.D. Mayergoyz, Mathematical Models of Hysteresis. Springer, New York 1991. | DOI | MR | Zbl

[12] L. Prandtl, Spannungsverteilung in plastischen Körpern. In: C.B. BIEZENO - J.M. BURGERS (eds.), Proceedings of the first International Congress for Applied Mechanics (Delft, 22-26 April 1924). J. Waltman Jr., Delft 1925, 43-54. | Jbk 51.0649.02

[13] L. Prandtl, Ein Gedankenmodell zur kinetischen Theorie der festen Körper. Z. Angew. Math. Mech., 8, 1928, 85-106. | Jbk 54.0847.04

[14] F. Preisach, Über die magnetische Nachwirkung. Z. Physik, 94, 1935, 277-302.

[15] A. Visintin (Ed.), Models of Hysteresis. Longman, Harlow 1993. | MR | Zbl

[16] A. Visintin, Differential Models of Hysteresis. Springer, Berlin 1994. | MR | Zbl

[17] A. Visintin, Six talks on hysteresis. C.R.M. Proceedings and Lecture Notes, 13, 1998, 207-236. | MR | Zbl

[18] A. Visintin, Quasi-linear hyperbolic equations with hysteresis. Ann. Inst. H. Poincaré, Nonlinear Analysis, 19, 2002, 451-476. | fulltext EuDML | fulltext mini-dml | DOI | MR | Zbl

[19] A. Visintin, Maxwell's equations with vector hysteresis. Arch. Rat. Mech. Anal., in press. | Zbl