Related papers: Detecting a hidden obstacle via the time domain en…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…
We study the one dimensional time dependent Schr\"{o}dinger equation for a potential step with $E < V_0$. We obtain the wave is not instantaneously reflected, but for a few moment of time the wave packet penetrate into inaccessible…
In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
In the frequency domain wave scattering problems, obstacles can be effectively replaced by point scatterers as soon as the wavelength of the incident wave exceeds significantly their diameter. The situation is less clear in the time domain,…
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
We investigate the internal observability of the wave equation with Dirichlet boundary conditions in tilings. The paper includes a general result relating internal observability problems in general domains to their tiles, and a discussion…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
Robust maritime obstacle detection is essential for fully autonomous unmanned surface vehicles (USVs). The currently widely adopted segmentation-based obstacle detection methods are prone to misclassification of object reflections and sun…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
It is generally believed that transformation optics based cloaking, besides rendering the cloaked region invisible to detection by scattering of incident waves, also shields the region from those same waves. We demonstrate a coupling…
This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…