Author(s)

Michael Grinfeld¹, Pavel Grinfeld²

¹The U.S. Army Research Laboratory, WMRD, Aberdeen Proving Ground, Harford County, USA.
²Mathematics 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.

Electric Current in Conductors, Irreversible Thermodynamics, Alegra Verification, Boundary Value Problems, Exact Solution

Grinfeld, M. and Grinfeld, P. (2022) Weak Wavefront Solutions of Maxwell’s Equations in Conducting Media. Journal of Applied Mathematics and Physics, 10, 190-199. doi: 10.4236/jamp.2022.101014.