Quasilinear hyperbolic equations with hysteresis

Augusto Visintin

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 235-247
  • ISSN: 1120-6330

Abstract

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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 ∂ 2 / ∂ ⁡ t 2 ⁢ u + F ⁢ u + A ⁢ u = f ; here 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.

How to cite

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Visintin, Augusto. "Quasilinear hyperbolic equations with hysteresis." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 235-247. <http://eudml.org/doc/252398>.

@article{Visintin2004,
abstract = {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.},
author = {Visintin, Augusto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hysteresis; Hysteresis operator; Quasilinear hyperbolic equations; Existence of weak solutions},
language = {eng},
month = {12},
number = {3-4},
pages = {235-247},
publisher = {Accademia Nazionale dei Lincei},
title = {Quasilinear hyperbolic equations with hysteresis},
url = {http://eudml.org/doc/252398},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Visintin, Augusto
TI - Quasilinear hyperbolic equations with hysteresis
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 235
EP - 247
AB - 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.
LA - eng
KW - Hysteresis; Hysteresis operator; Quasilinear hyperbolic equations; Existence of weak solutions
UR - http://eudml.org/doc/252398
ER -

References

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  12. PRANDTL, L., 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., Delft1925, 43-54. JFM51.0649.02
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  14. PREISACH, F., Über die magnetische Nachwirkung. Z. Physik, 94, 1935, 277-302. 
  15. VISINTIN, A., Models of Hysteresis. Longman, Harlow1993. Zbl0785.00016MR1235109
  16. VISINTIN, A., Differential Models of Hysteresis. Springer, Berlin1994. Zbl0820.35004MR1329094
  17. VISINTIN, A., Six talks on hysteresis. C.R.M. Proceedings and Lecture Notes, 13, 1998, 207-236. Zbl0918.35067MR1619117
  18. VISINTIN, A., Quasi-linear hyperbolic equations with hysteresis. Ann. Inst. H. Poincaré, Nonlinear Analysis, 19, 2002, 451-476. Zbl1027.35076MR1912263DOI10.1016/S0294-1449(01)00086-5
  19. VISINTIN, A., Maxwell's equations with vector hysteresis. Arch. Rat. Mech. Anal., in press. Zbl1145.78003

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