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We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a…
This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
This work concerns the design of perfectly conducting objects that are invisible to an incident transverse magnetic plane wave. The object in question is a finite planar waveguide with a finite periodic array of barriers. By optimizing this…
Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce…
Although the black holes are an integral part of the standard model of astrophysics and cosmology, their existence poses some serious fundamental problems. In recent years, several horizonless compact object models were proposed to address…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…
Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and…
We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave…
The quantum shutter approach to tunneling time scales (G. Garc\'{\i }a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type…
Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…
Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevence to the transmission of…
The wave equation on a bounded domain of $\R^{n}$ with non homogeneous boundary Dirichlet data or sources supported on a subset of the boundary is considered. We analyze the problem of observing the source out of boundary measurements done…
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…
This paper approaches, using structural complexity theory, the question of whether there is a chasm between knowing an object exists and getting one's hands on the object or its properties. In particular, we study the nontransparency of…