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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…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
Strating with the Maxwell's equations in presence of electric and magnetic sources in an isotropic homogenous medium, we have derived the various quantum equations of dyons in consistent and manifest covariant way. It has been shown that…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…
We consider the time-harmonic Maxwell equations with impedance boundary conditions on a bounded Lipschitz domain $\Omega$ with analytic boundary $\Gamma$. We suppose that $\Omega$ consists of multiple subdomains, and that the permeability…
The Euler-Maxwell system as a hydrodynamic model for plasma physics to describe the dynamics of the compressible electrons in a constant charged non-moving ion background is studied. The global smooth flow with small amplitude is…
We present a stable and convergent mixed finite element method (MFEM) for the linear regularized 13-moment (R13) equations in rarefied gas dynamics. Unlike existing methods that require stabilization via penalty terms, our scheme achieves…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial variables and random stationary in time. We assume that the…
We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of…
This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…