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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2004_9_15_3-4_a6,
     author = {Visintin, Augusto},
     title = {Quasilinear hyperbolic equations with hysteresis},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {235--247},
     year = {2004},
     volume = {Ser. 9, 15},
     number = {3-4},
     zbl = {1162.35424},
     mrnumber = {MR2148882},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a6/}
}
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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/