Related papers: The Static Maxwell System in Three Dimensional Inh…
This paper extends approach of recent author's paper devoted to special classes of exact solutions of the static Maxwell system in inhomogeneous isotropic media and new generalizations of the Cauchy-Riemann system in $\mathbb R^3$. Two…
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand…
The paper is concerned with the inverse scattering problem for Maxwell's equations in three dimensional anisotropic periodic media. We study a new imaging functional for fast and stable reconstruction of the shape of anisotropic periodic…
We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.
For the system of Maxwell equations of electromagnetism in an $l$-periodic composite medium of overall size $L$ ($0<l<L<\infty$), in the low-frequency quasistatic approximation, we develop an electromagnetic version of strain-gradient…
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
We prove Strichartz estimates for Maxwell equations in media in the fully anisotropic case with H\"older-continuous coefficients. To this end, we use the FBI transform to conjugate the problem to phase space. After reducing to a scalar…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that…
Two-dimensional Maxwell-Vlasov equilibria with finite electric fields, axial ("toroidal") plasma flow and isotropic pressure are constructed in plane geometry by using the quasineutrality condition to express the electrostatic potential in…
Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter…
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable (see…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
In this paper, we explore the existence of various non-singular compact stellar solutions influenced by the Maxwell field within the matter-geometry coupling based modified gravity. We start this analysis by considering a static spherically…
In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…
In this paper we are concerned with plane wave discontinuous Galerkin (PWDG) methods for Helmholtz equation and time-harmonic Maxwell equations in three-dimensional anisotropic media, for which the coefficients of the equations are matrices…
We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the…