A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D geometries with the help of a continuous approximation of the electromagnetic field. In this paper, we investigate how their framework can be adapted to compute the solution to the time-dependent Maxwell equations. In addition, we propose some exten...

The properties of spinors and vectors in (2 + 2) space split quaternions are studied. Quaternionic representation rotations naturally separates two SO(2,1) subgroups the full group symmetry norms quaternions, SO(2,2). One them represents symmetries three-dimensional Minkowski space-time. Then, second subgroup, generated by additional time-like coordinate from basis can be viewed as internal mod...

New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and non-trivial charges are proved. We use FBI transform to carry out analysis phase space. For this purpose, equations conjugated a of half-wave coefficients. system, similarly derived as previous work by Tataru on scalar wave improve local well-posedness theory quasilinear dimensions.

We show that localized (nonevanescent) solutions to Maxwell equations exist, which propagate without distortion along normal waveguides with superluminal speed.