We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in [16], we propose an algorithm based on the use of bivariate B-splines spaces suitably adapted to electromagnetics. We construct B-splines spaces of variable interelement regularity on the parametric domain. These spaces (and their push-forwar...

This paper is devoted to the study of relativistic Vlasov-Maxwell system in space dimension three. For a class large initial data, we prove global existence classical solution with sharp decay estimates. The Maxwell field allowed be arbitrarily and density distribution assumed small rate $$(1+|x|+|v|)^{-9-}$$ . In particular, there no restriction on support data.

We consider a modified version of the Vlasov-Maxwell system in which the usual Maxwell fields are replaced by their retarded parts. We show that solutions of this modified system exist globally for a small number of particles and that they describe a system without incoming radiation.

The method based on the Horský-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.

We analyze the interaction of an electromagnetic spike (one cycle) with a thin layer of ferroelectric medium with two equilibrium states. The model is the set of Maxwell equations coupled to the undamped LandauKhalatnikov equation, where we do not assume slowly varying envelopes.

The Maxwell-Dirac equations are the equations for electronic matter, the “classical” theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell-Dirac system has ψ = eφ, with φ independent of t. The system is said to be isolated if the independent variables obey quite weak regularity and decay conditions. In this p...

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Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss’s laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to der...

Due to the mathematical complexity of the Boltzmann equation for inelastic hard spheres, a kinetic model has recently been proposed whereby the collision rate (which is proportional to the relative velocity for hard spheres) is replaced by an average velocity-independent value. The resulting inelastic Maxwell model has received a large amount of recent interest, especially in connection with th...