Related papers: On the solution of the static Maxwell system in ax…
We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions…
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…
A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…
We propose a simple quaternionic reformulation of Maxwell's equations for inhomogeneous media and use it in order to obtain new solutions in a static case.
We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…
This paper extends approach of our joint paper with K\"{a}hler and recent paper of the author, published in 2021, on problems of the static Maxwell system in three dimensional inhomogeneous media. Applied pseudoanalytic function theory…
We carry out the homogenization of time-harmonic Maxwell's equations in a periodic, layered structure made of two-dimensional (2D) metallic sheets immersed in a heterogeneous and in principle anisotropic dielectric medium. In this setting,…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the perfect conductivity boundary conditions. It is assumed that the dielectric permittivity and the magnetic permeability…
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…
We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
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…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
Exact solutions to the static equilibrium magnetohydrodynamic equations are presented and discussed for both axially and helically reduced systems. For both symmetries, physical restrictions on the solutions are discussed and it is seen…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
In this work we study the electric field of a dipole immersed in a medium with permittivity controlled by a real scalar field which is non-minimally coupled to the Maxwell field. We model the system with an interesting function, which…
This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the…