On Maxwell equations with the Preisach hysteresis operator: The one- dimensional time-periodic case. (English) Zbl 0701.35098

Two energy functionals for the Preisach hysteresis operator are used for proving the existence of weak periodic solutions of the one-dimensional system of Maxwell equations with hysteresis under periodic forcing. In terms of the geometry of the hysteresis loops, these two functionals correspond to their area and curvature, respectively. In this model, the speed of propagation of waves does not exceed the velocity of light.
Reviewer: P.Krejčí


35L60 First-order nonlinear hyperbolic equations
35B10 Periodic solutions to PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35Q60 PDEs in connection with optics and electromagnetic theory
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