Decay of solutions of Maxwell–Klein–Gordon equations with arbitrary Maxwell field

Finite Energy Superluminal Solutions of Maxwell Equations

We exhibit exact finite energy superluminal solutions of Maxwell equations in vacuum. e-mail: [email protected] e-mail: [email protected] or [email protected] 1 Recently, some papers [1,2] appeared in the literature showing that in some hypotetical media there is the possibility for the existence of superluminal electromagnetic pulses (solutions of Maxwell equations) such their fronts tr...

Solutions of the cylindrical nonlinear Maxwell equations.

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical n...

Strong Cosmic Censorship for Solutions of the Einstein-maxwell Field Equations with Polarized Gowdy Symmetry

A proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum G...

Some Variational Problems for Field Equations Coupled with Maxwell Equations

Exponential decay for Maxwell equations with a boundary memory condition

We study the asymptotic behavior of the solution of the Maxwell equations with the following boundary condition of memory type Eτ (t) = η0H(t)× n + ∫ ∞ 0 η(s)H(t− s)× n ds. We consider a ‘Graffi’ type free energy and we prove that, if the kernel η satisfies the condition η′′ + κ η′ > 0 and the domain Ω is strongly star shaped, then the energy of the solution exponentially decays. We also prove ...