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We give a general family of electromagnetic boundary conditions applicable to arbitrary space--time interfaces between electromagnetic media, which include the known space--only and time--only boundary conditions as special cases. These…
In this paper we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localised modes in such a setting. A crucial assumption in this paper is time-modulated material parameters.…
The goal of this paper is to prove a stable determination of the coefficients for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary measurements.
We present the concept of time-domain bound states in continuum. We show that a rapid judiciously-designed temporal modulation of the refractive index in a spatially homogenous medium gives rise to a bound state in time embedded in a…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of…
We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We consider the time-harmonic Maxwell equations posed in $\mathbb{R}^3$. We prove a priori bounds on the solution for $L^\infty$ coefficients $\epsilon$ and $\mu$ satisfying certain monotonicity properties, with these bounds valid for…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
Spatially localized oscillations in periodically forced systems are intriguing phenomena. They may occur in spatially homogeneous media (oscillons), but quite often emerge in heterogeneous media, such as the auditory system, where localized…
In this work we study the classical electrodynamics in homogeneous conducting and nonconducting time-dependent linear media in the absence of charge sources. Surprisingly, we find that the time dependence of the permittivity gives rise to…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in time Strichartz estimates if the domain is strictly convex.
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…