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Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\alpha$, with each $D_\alpha$ a homogeneous elastic medium. One typical…

Analysis of PDEs · Mathematics 2017-04-13 Cătălin I. Cârstea , Naofumi Honda , Gen Nakamura

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

Mathematical Physics · Physics 2019-08-06 A. Merzon , P. Zhevandrov , J. E. De la Paz Méndez , T. J. Villalba Vega

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential…

Analysis of PDEs · Mathematics 2020-07-23 Habib Zribi

Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…

Analysis of PDEs · Mathematics 2013-05-07 Jiaqing Yang , Bo Zhang

A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…

Analysis of PDEs · Mathematics 2017-05-01 A. V. Shanin , A. I. Korolkov

We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with…

Analysis of PDEs · Mathematics 2018-01-17 Plamen Stefanov , Gunther Uhlmann , Andras vasy

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…

Analysis of PDEs · Mathematics 2021-02-19 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng

The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

An inverse problem for the wave equation outside an obstacle with a {\it dissipative boundary condition} is considered. The observed data are given by a single solution of the wave equation generated by an initial data supported on an open…

Analysis of PDEs · Mathematics 2016-07-22 Masaru Ikehata

The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally…

Analysis of PDEs · Mathematics 2025-06-10 Lauri Oksanen , Rakesh , Mikko Salo

The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…

Analysis of PDEs · Mathematics 2021-03-16 Masaru Ikehata

We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

Analysis of PDEs · Mathematics 2018-09-19 Freddy J. F. Symons

This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on which a Neumann boundary condition is imposed. A novel integral equation formulation is…

Numerical Analysis · Mathematics 2024-12-20 Fenglong Qu , Bo Zhang , Haiwen Zhang

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…

Analysis of PDEs · Mathematics 2015-06-03 Mourad Bellassoued , Mourad Choulli , Aymen Jbalia

We are concerned with the time-harmonic elastic scattering due to an inhomogeneous elastic material inclusion located inside a uniformly homogeneous isotropic medium. We establish a sharp stability estimate of logarithmic type in…

Analysis of PDEs · Mathematics 2021-11-25 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng

We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…

Analysis of PDEs · Mathematics 2026-01-13 Amandine Boucart , Sonia Fliss , Laure Giovangigli

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…

Optics · Physics 2019-05-22 H. M. Alkhoori , A. Lakhtakia , J. K. Breakall , C. F. Bohren

We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…

Analysis of PDEs · Mathematics 2015-03-17 Mourad Choulli , Kaïs Ammari

In even dimensional Euclidean scattering, the resonances lie on the logarithmic cover of the complex plane. This paper studies resonances for obstacle scattering in ${\mathbb R}^d$ with Dirchlet or admissable Robin boundary conditions, when…

Mathematical Physics · Physics 2014-09-29 T. J. Christiansen