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A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a…
We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell's equations that preserves this symmetry. This new set of equations…
We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…
We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…