相关论文: A limiting absorption principle for Helmholtz syst…
This paper investigates the following question: given a Galerkin matrix corresponding to a finite-element discretisation of either the Helmholtz or time-harmonic Maxwell equations with variable coefficients, suppose that the coefficients of…
We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…
We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…
We analyze the Helmholtz equation in a complex domain. A sound absorbing structure at a part of the boundary is modelled by a periodic geometry with periodicity $\varepsilon>0$. A resonator volume of thickness $\varepsilon$ is connected…
One-dimensional lamellar gratings allow a particularly efficient way for solving Maxwell's equations by expanding the electromagnetic field in the basis of exact eigenmodes of the Helmholtz equation. Then, the solution can be expressed…
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
An advanced full-wave time-domain numerical model for reverse saturable absorption (RSA) is presented and verified against established methods. Rate equations, describing atomic relaxations and excitation dynamics, are coupled to Maxwell…
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M.…
We prove the $L^p-L^q$ $(1<p\leqslant 2\leqslant q<+\infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by using an integro-differential operator in time and any…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
We introduce a novel multi-resolution Localized Orthogonal Decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges the concepts of LOD and operator-adapted wavelets…
Using a generalisation of the classical notion of Dirichlet-to-Neumann map and the related formulae for the resolvents of boundary-value problems, we analyse the asymptotic behaviour of solutions to a "transmission problem" for a…
We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…
We study the $L^p-L^q$-type uniform resolvent estimates for 2D-Schr\"odinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an application, we prove localization estimates for the…
Time-resolved spectroscopy provides the main tool for analyzing the dynamics of excitonic energy transfer in light-harvesting complexes. To infer time-scales and effective coupling parameters from experimental data requires to develop…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
We prove the existence of $L^2$ solutions to the Helmholtz equation $(-\Delta - 1)u = f$ in ${\mathbb R}^n$ assuming the given data $f$ belongs to $L^{(2n+2)/(n+5)}({\mathbb R}^n)$ and satisfies the "Fredholm condition" that $\hat{f}$…
In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the…
We propose a new single frequency reverse time migration (RTM) algorithm for imaging extended targets using electromagnetic waves. The imaging functional is defined as the imaginary part of the cross-correlation of the Green function for…