In this paper we continue the investigation of the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations. In particular we extend some previous results about the Cauchy problem and the quasi-stationary limit to the case where the magnetic permeability and the electric permittivity are variable.

In this report we investigate the continuous dependence with respect to the initial data of the solutions for the 1D and 1.5D relativistic Vlasov-Maxwell system. More precisely we prove that these solutions propagate with finite speed. We formulate our results in the framework of mild solutions, i.e., the particle densities are solutions by characteristics and the electro-magnetic fields are Li...

In this paper the Maxwell field theory is considered on a closed and orientable Riemann surface of genus h > 1. The solutions of the Maxwell equations corresponding to nontrivial values of the first Chern class are explicitly constructed for any metric in terms of the prime form.

It is shown how the gauge of the “regular finite initial value problem at spacelike infinity” can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are constructed with the objective of obtaining information about the smoothness near spacelike and null infinity of a wide class of solutions to the Maxwell equations.

The notion of B-spline based discrete differential forms is recalled and along with a Finite Element Hodge operator, it is used to design new numerical methods for solving the Vlasov-Poisson equations. Answer’s to the referees’ questions Aurore Back and Eric Sonnendrücker April 12, 2013 We thank the referees for the careful reading of our manuscript and for many interesting comments that helped...

We consider the two-dimensional Maxwell s equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ‘‘small-cell’’ time-step restriction in the expli...

We consider a class of inverse source problems for the parabolic approximation to the Maxwell equations using a Bayesian approach.

An example of application of the specialized computer algebra system GRGEC to the searching for solutions to the source-free Maxwell and Einstein–Maxwell equations is demonstrated. The solution involving five arbitrary functions of two variables is presented in explicit form (up to quadratures).

The scalable iterative solution of strongly coupled three-dimensional incompressible resistive magnetohydrodynamics (MHD) equations is very challenging because disparate time scales arise from the electromagnetics, the hydrodynamics, as well as the coupling between these systems. This study considers a mixed finite element discretization of a dual saddle point formulation of the incompressible ...

The generalized Einstein Maxwell field equations which arise from a truncated bosonic part of the low energy string gravity effective action in four dimensions (the so called Einstein-Maxwell axion dilaton theory) are considered. The integrable structure of these field equations for D = 4 space-times with two commuting isometries is elucidated. We express the dynamical part of the reduced equat...