Related papers: Localizing acoustic and electromagnetic waves in s…
We study acoustic propagation in one dimensional water ducts containing many air-filled blocks. The acoustic band structures for the periodic arrangements of the blocks is calculated, whereas the transmission for various random…
We study homogenization of multiscale Maxwell wave equation that depends on $n$ separable microscopic scales in a domain $D\subset{\mathbb R}^d$ on a finite time interval $(0,T)$. Due to the non-compactness of the embedding of…
In this letter, we investigate the statistical properties of electromagnetic signals after different times of duration within one-dimensional local-disordered time-varying cavities, where both spatial and temporal disorders are added. Our…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…
Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation. Under the assumption that the relaxation kernel decays…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…
We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…
We study the problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $T>0$ and $\Omega$ a $ \mathcal C^2$ bounded domain of…
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…
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
The geometries of surface wave modes are determined by the highly nontrivial interplay of capillarity and wetting effects at the boundaries of their domain. Aside from idealised scenarios, this commonly leads to unknown boundary conditions,…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
In this paper, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We…
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…
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…