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Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…

Analysis of PDEs · Mathematics 2023-01-05 Yves Capdeboscq , Tianrui Dai

The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…

Mathematical Physics · Physics 2016-09-07 A. G. Ramm

We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…

Analysis of PDEs · Mathematics 2024-09-05 Isaac Harris , Andreas Kleefeld , Heejin Lee

We investigate a one-dimensional nonlinear wave system which arises from a variational principle modeling a type of cholesteric liquid crystals. The problem treated here is the Cauchy problem for the same wave speed case with initial data…

Analysis of PDEs · Mathematics 2019-12-24 Yanbo Hu , Huijuan Song

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

Numerical Analysis · Mathematics 2025-08-12 Iulian Cîmpean , Andreea Grecu , Liviu Marin

We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…

Analysis of PDEs · Mathematics 2024-09-05 Emilia Blåsten , Petri Ola , Lassi Päivärinta

This paper studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem to reconstruct Stekloff eigenvalues is investigated using a new integral…

Mathematical Physics · Physics 2019-09-04 Juan Liu , Yanfang Liu , Jiguang Sun

In this paper, we will discuss the use of a Sampling Method to reconstruct impenetrable inclusions from Electrostatic Cauchy data. We consider the case of a perfectly conducting and impedance inclusion. In either case, we show that the…

Analysis of PDEs · Mathematics 2021-02-10 Isaac Harris

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…

Analysis of PDEs · Mathematics 2017-05-12 Kiril Datchev , Maarten V. de Hoop

We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…

Analysis of PDEs · Mathematics 2026-05-21 Sarah Eberle-Blick , Jochen Moll

We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of…

Analysis of PDEs · Mathematics 2024-07-26 Boya Liu , Teemu Saksala , Lili Yan

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

Analysis of PDEs · Mathematics 2024-06-04 Xiaoxu Xu , Guanghui Hu

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…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…

Numerical Analysis · Mathematics 2017-10-16 Michael V. Klibanov , Dinh-Liem Nguyen , Loc H. Nguyen

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…

Analysis of PDEs · Mathematics 2021-11-12 Masaru Ikehata

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic…

Analysis of PDEs · Mathematics 2018-10-31 M. N. Demchenko

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered…

Numerical Analysis · Mathematics 2018-04-17 Xiaoli Liu , Bo Zhang , Haiwen Zhang

We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…

Analysis of PDEs · Mathematics 2019-04-09 J Liu , X. Liu , J. Sun