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The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…

Numerical Analysis · Mathematics 2017-06-07 Dinh-Liem Nguyen , Michael V. Klibanov , Loc H. Nguyen , Aleksandr E. Kolesov , Michael A. Fiddy , Hui Liu

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

In this paper, we are interested to an inverse Cauchy problem governed by the Stokes equation, called the data completion problem. It consists in determining the unspecified fluid velocity, or one of its components over a part of its…

Numerical Analysis · Mathematics 2021-12-30 A. Chakib , A. Nachaoui , M. Nachaoui , H. Ouaissa

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information…

Numerical Analysis · Mathematics 2016-01-20 Henrik Garde , Kim Knudsen

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…

Analysis of PDEs · Mathematics 2026-04-14 Jialei Li , Xiaodong Liu

An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…

Mathematical Physics · Physics 2007-12-04 Michael V Klibanov , Sergey I Kabanikhin , Dmitriy V Nechaev , Andrey V Kuzhuget

In this work, we investigate a class of elliptic inverse problems and aim to simultaneously recover multiple inhomogeneous inclusions arising from two different physical parameters, using very limited boundary Cauchy data collected only at…

Numerical Analysis · Mathematics 2020-06-05 Yat Tin Chow , Fuqun Han , Jun Zou

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

Analysis of PDEs · Mathematics 2007-05-23 Kenrick Bingham , Yaroslav Kurylev , Matti Lassas , Samuli Siltanen

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…

Analysis of PDEs · Mathematics 2019-09-02 Maarten V. de Hoop , Alexei Iantchenko , Robert D. van der Hilst , Jian Zhai

We discuss the Cauchy problem for anisotropic wave equations. Precisely, we address the question to know which kind of Cauchy data on the lateral boundary are necessary to guarantee uniqueness of solutions of an anisotropic wave equation.…

Analysis of PDEs · Mathematics 2021-07-09 Mourad Bellassoued , Mourad Choulli

We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very…

Numerical Analysis · Mathematics 2025-11-12 Bangti Jin , Fengru Wang , Jun Zou

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , B. Tomas Johansson , Leonidas Mindrinos

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lam\'{e} operator…

Mathematical Physics · Physics 2019-11-26 Guanghui Hu , Andrea Mantile , Mourad Sini , Tao Yin

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we focus on Love waves. Under certain generic conditions, we establish uniqueness and present a reconstruction scheme for the S- wavespeed…

Analysis of PDEs · Mathematics 2019-08-29 Maarten V. de Hoop , Alexei Iantchenko , Robert D. van der Hilst , Jian Zhai

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rough surface from the scattered near-field Cauchy data generating by point sources and…

Numerical Analysis · Mathematics 2018-05-01 Xiaoli Liu , Bo Zhang , Haiwen Zhang

We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We…

Analysis of PDEs · Mathematics 2025-09-16 Sebastian Acosta , Benjamin Palacios