scholarly journals Internal stabilization of Maxwell's equations in heterogeneous media

2005 ◽  
Vol 2005 (7) ◽  
pp. 791-811 ◽  
Author(s):  
Serge Nicaise ◽  
Cristina Pignotti
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Heterogeneous Media ◽  
Space Variable ◽  
Smooth Boundary ◽  
Variable Coefficients ◽  
Bounded Region ◽  
Scalar Wave ◽  
Internal Stabilization

We consider the internal stabilization of Maxwell's equations with Ohm's law with space variable coefficients in a bounded region with a smooth boundary. Our result is mainly based on an observability estimate, obtained in some particular cases by the multiplier method, a duality argument and a weakening of norm argument, and arguments used in internal stabilization of scalar wave equations.

scholarly journals DIFFRACTION OF BLOCH WAVE PACKETS FOR MAXWELL'S EQUATIONS

2013 ◽  
Vol 15 (06) ◽  
pp. 1350040 ◽  
Author(s):  
GRÉGOIRE ALLAIRE ◽  
MARIAPIA PALOMBARO ◽  
JEFFREY RAUCH
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Approximate Solutions ◽  
Bloch Wave ◽  
System Structure ◽  
Periodic Medium ◽  
Scalar Wave ◽  
Infinite Dimensional

We study, for times of order 1/h, solutions of Maxwell's equations in an [Formula: see text] modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schrödinger equation given by the quadratic approximation of the Bloch dispersion relation. A weak ray average hypothesis guarantees stability. Compared to earlier work on scalar wave equations, the generator is no longer elliptic. Coercivity holds only on the complement of an infinite-dimensional kernel. The system structure requires many innovations.

WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS

2012 ◽  
Vol 14 (05) ◽  
pp. 1250032 ◽  
Author(s):  
BRUNO FRANCHI ◽  
MARIA CARLA TESI
Keyword(s):  
Vector Potential ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Evolution Equations ◽  
Differential Forms ◽  
Higher Order ◽  
Carnot Groups ◽  
New Class ◽  
Euclidean Setting

In this paper we define Maxwell's equations in the setting of the intrinsic complex of differential forms in Carnot groups introduced by M. Rumin. It turns out that these equations are higher-order equations in the horizontal derivatives. In addition, when looking for a vector potential, we have to deal with a new class of higher-order evolution equations that replace usual wave equations of the Euclidean setting and that are no more hyperbolic. We prove equivalence of these equations with the "geometric equations" defined in the intrinsic complex, as well as existence and properties of solutions.

scholarly journals Extension of the electrodynamics in the presence of the axion and dark photon

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950012 ◽  
Author(s):  
Fa Peng Huang ◽  
Hye-Sung Lee
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Dark Photon

We present the extended electrodynamics in the presence of the axion and dark photon. We derive the extended versions of Maxwell’s equations and dark Maxwell’s equations (for both massive and massless dark photons) as well as the wave equations. We discuss the implications of this extended electrodynamics including the enhanced effects in the particle conversions under the external magnetic or dark magnetic field. We also discuss the recently reported anomaly in the redshifted 21 cm spectrum using the extended electrodynamics.

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.

An HDG method for Maxwell’s equations in heterogeneous media

2020 ◽  
Vol 368 ◽  
pp. 113178
Author(s):  
Liliana Camargo ◽  
Bibiana López-Rodríguez ◽  
Mauricio Osorio ◽  
Manuel Solano
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Heterogeneous Media
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