Maxwell’s Equations. Antenna Problems
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 . 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.
KeywordsScalar Product Variational Inequality Electric Charge Strong Solution Polarizable Medium
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