Related papers: Strichartz estimates for Maxwell equations in medi…
The propagation of waves through microstructured media with periodically arranged inclusions has applications in many areas of physics and engineering, stretching from photonic crystals through to seismic metamaterials. In the…
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,…
Maxwell's equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schr\"odinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include…
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
In this work, we prove that in anisotropic media possessing cubic, transversely isotropic, orthotropic, and monoclinic symmetries, there exist non-ellipsoidal inclusions that can transform particular quadratic eigenstrains into quadratic…
Taking as starting point the planar model arising from the dimensional reduction of the Abelian-Higgs Carroll-Field-Jackiw model, we write down and study the extended Maxwell equations and the corresponding wave equations for the…
We derive basic equations of electromagnetic fields in fractal media which are specified by three indepedent fractal dimensions {\alpha}_{i} in the respective directions x_{i} (i=1,2,3) of the Cartesian space in which the fractal is…
In this paper, we introduce a finite element method employing the Ned\'el\'ec element space for solving the Maxwell's transmission eigenvalue problem in anisotropic media. The well-posedness of the source problems are derived using $\mathbb…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…
In anisotropic media, the standard perfectly matched layer (PML) technique suffers irrevocable instability in terminating the unbounded problem domains. It remains an open question whether a stable PML-like absorbing boundary condition…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
In this paper we initiate the mathematical analysis of a system of nonlinear Stochastic Partial Differential equations describing the motion of turbulent Non-Newtonian media in the presence of fluctuating magnetic field. The system is…
Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the…
We improve our previous result [L. Molinet and T. Tanaka, Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations, J. Funct. Anal. 283 (2022), 109490] on the Cauchy problem for one dimensional…
For some anisotropic wave models, the PML (perfectly matched layer) method of open boundaries can become polynomially or exponentially unstable in time. In this work we present a new method of open boundaries, the phase space filter, which…
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.
When anisotropy is involved, the wave equation becomes simultaneous partial differential equations that are not easily solved. Moreover, when the anisotropy occurs due to both permittivity and permeability, these equations are insolvable…