Shock Fronts in Non-Polar Electro-Conducting Media  

作　　者：Michael Grinfeld Pavel Grinfeld Michael Grinfeld;Pavel Grinfeld(The U.S. Army Research Laboratory, Aberdeen Proving Ground, Harford County, USA;Department of Mathematics, Drexel University, Philadelphia, USA)

机构地区：[1]The U.S. Army Research Laboratory, Aberdeen Proving Ground, Harford County, USA [2]Department of Mathematics, Drexel University, Philadelphia, USA

出　　处：《Journal of Applied Mathematics and Physics》2022年第4期1055-1065,共11页应用数学与应用物理（英文）

摘　　要：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.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 

分 类 号：O17[理学—数学]