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Weak Wavefront Solutions of Maxwell’s Equations in Conducting Media

Journal of Applied Mathematics and Physics 2022年第1期10卷 190-199页

作者： Michael Grinfeld Pavel Grinfeld The U.S. Army Research Laboratory WMRD Aberdeen Proving Ground Harford County USA Mathematics Department Drexel University Philadelphia USA

We analyze the propagation of electromagnetic fronts in unbounded electric conductors. Our analysis is based on the Maxwell model of electromagnetism that includes the displacement current and Ohm’s law in its simplest forms. A weak electromagnetic front is a propagating interface at which the electromagnetic field remains continuous while its first- and higher-order derivatives experience finite jump discontinuities. Remarkably, analysis of such fronts can be performed autonomously, i.e. strictly in terms of the quantities defined on the front. This property opens the possibility of establishing exact analytical solutions of the exact Maxwell system along with the evolution of the front.

关键词： electric current in conductors Irreversible Thermodynamics Alegra Verification Boundary Value Problems Exact Solution

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Shock Fronts in Non-Polar Electro-Conducting Media

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1055-1065页

作者： Michael Grinfeld Pavel Grinfeld The U.S. Army Research Laboratory Aberdeen Proving Ground Harford County USA Department of Mathematics Drexel University Philadelphia USA

We analyze the propagation of electromagnetic fronts in unbounded electric conductors. Our model is based on the Maxwell model of electromagnetism, which includes the displacement current and Ohm’s law in its simplest forms. The shock-like electromagnetic front is a propagating surface, across which the electric and magnetic fields, as well as their higher temporal and spatial derivatives, experience finite jumps. The shock-like fronts are essentially different as compared with the weak fronts;in particular, the bulk Maxwell equations are essentially insufficient for the analysis of the shock-like fronts, and they should be amended we the physical jump conditions. We choose these additional conditions by using conditions similar to those suggested by Heaviside. We derive the basic shock intensity relationships implied by this model.

关键词： electric current in conductors Boundary Value Problems Exact Solution Ray-Equations

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