Abstract
The phenomena of electromagnetism can lead to variational inequalities, either with Maxwell’s equations in a polarizable medium or, when the phenomena are coupled, with the mechanics of Bingham fluids yielding the magnetodynamics of Bingham fluids. This second possibility is treated in Duvaut-Lions [7]. The present chapter is devoted to unilateral problems connected with Maxwell’s equations. Since we cannot refer to a unified exposition of the classical phenomena of electromagnetism, we will set up equations for the phenomena in Section 2 and develop a mathematical theory for the classical solutions in Sections 4–6. This theory is indispensable for the subsequent treatment of Maxwell’s equations in a polarizable medium. Section 3 is a presentation of the physical problems under consideration.
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© 1976 Springer-Verlag Berlin Heidelberg
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Duvaut, G., Lions, J.L. (1976). Maxwell’s Equations. Antenna Problems. In: Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66165-5_7
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DOI: https://doi.org/10.1007/978-3-642-66165-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66167-9
Online ISBN: 978-3-642-66165-5
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