Quasilinear hyperbolic equations with hysteresis (Q5920640)

Summary: Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation \((\partial \,^{2}/\partial t^{2})[u+{\mathcal F}\,(u)]+Au=f;\) 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.