Finite speed of propagations of the electromagnetic field in nonlinear isotropic dispersive mediums

A dispersive estimate for the linear wave equation with an electromagnetic potential

We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a priori estimates that imply, in particular, a dispersive estimate.

Asymptotic behavior of dispersive electromagnetic waves in bounded domains

We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the boundedness of the associated semigroup. Further the exponential or polynomial decay of the energy is proved under suitable sufficient conditions. Finally, several illustrative examples are presented.

Dispersive estimates for 2D-wave equations with critical potentials

We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In particular, the diamagnetic phenomenon allows to consider negative electric potential which can be singular in the same fashion as the inverse-square potential. We prove sharp time-decay estimates in the purely magnetic case, and Strichartz estimates for the complete model, involving a critical electromagnetic field.

Electromagnetic wave propagation in media consisting of dispersive metamaterials

We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drude's and Lorentz' models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drude's model to illustrate its dispersive behaviour.

电磁色散波的数学模型：综述

Mathematical models for dispersive electromagnetic waves: an overview

本文综述了电磁波在色散各向同性介质中的数学模型，强调物理要求与数学性质的联系，探讨非耗散性和被动性，并通过能量技术、谱理论和平面波色散分析研究模型。

非线性麦克斯韦方程在具有界面的色散材料中的适定性与指数稳定性

Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface

本文研究具有界面的色散材料中非线性麦克斯韦方程的适定性与指数稳定性，通过演化方程框架在加权函数空间中建立适定性并给出实现指数稳定的条件。