Existence of global solutions to one-dimensional nonlinear Maxwell’s equations

1990 ◽  
Vol 7 (3) ◽  
pp. 399-421
Author(s):  
Fumioki Asakura
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Global Solutions ◽  
One Dimensional

Exact solutions of the three-dimensional scalar wave equation and Maxwell's equations from the approximate solutions in the wave zone through the use of the Radon transform

1989 ◽  
Vol 422 (1863) ◽  
pp. 351-365 ◽  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Radon Transform ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Asymptotic Solutions ◽  
Scalar Wave ◽  
Wave Zone ◽  
One Dimensional

In our earlier paper we have shown that the solutions of both the three-dimensional scalar wave equation, which is also the three-dimensional acoustic equation, and Maxwell’s equations have forms in the wave zone, which, except for a factor 1/ r , represent one-dimensional wave motions along straight lines through the origin. We also showed that it is possible to reconstruct the exact solutions from the asymptotic forms. Thus we could prescribe the solutions in the wave zone and obtain the exact solutions that would lead to them. In the present paper we show how the exact solutions can be obtained from the asymptotic solutions and conversely, through the use of a refined Radon transform, which we introduced in a previous paper. We have thus obtained a way of obtaining the exact three-dimensional solutions from the essentially one-dimensional solutions of the asymp­totic form entirely in terms of transforms. This is an alternative way to obtaining exact solutions in terms of initial values through the use of Riemann functions. The exact solutions that we obtain through the use of the Radon transform are causal and therefore physical solutions. That is, these solutions for time t > 0 could have been obtained from the initial value problem by prescribing the solution and its time-derivative, in the acoustic case, and the electric and magnetic fields, in the case of Maxwell’s equations, at time t = 0. The role of time in the relation between the exact solutions and in the asymptotic solutions is made very explicit in the present paper.

scholarly journals Global solutions of Maxwell's equations in an electromagnetic field with a temperature-dependent electrical conductivity

1994 ◽  
Vol 5 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Hong-Ming Yin
Keyword(s):  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Global Solutions ◽  
Global Solvability ◽  
Temperature Dependent ◽  
Strongly Coupled ◽  
Temperature Dependent Electrical Conductivity ◽  
Effects Of Temperature

This paper deals with Maxwell's equations in a quasi-stationary electromagnetic field subject to the effects of temperature. This model is encountered in the penetration of a magnetic field in substances where the electrical conductivity depends on the temperature. Similar phenomena also occur in some industrial problems such as the thermistor. Taking the effect of Joule heating into the consideration, we obtain a strongly coupled nonlinear system. Global solvability is established for this system.

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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