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We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

Numerical Analysis · Mathematics 2018-05-23 Mirza Karamehmedović , Adrian Kirkeby , Kim Knudsen

We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…

Analysis of PDEs · Mathematics 2018-09-03 Mozhgan Nora Entrekhabi , Victor Isakov

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…

Numerical Analysis · Mathematics 2015-06-19 Thorsten Hohage , Frederic Weidling

In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…

Analysis of PDEs · Mathematics 2025-03-07 Pu-Zhao Kow , Mikko Salo , Sen Zou

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…

Analysis of PDEs · Mathematics 2018-06-12 Mourad Choulli , Faouzi Triki

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…

Analysis of PDEs · Mathematics 2012-05-31 Habib Ammari , Hajer Bahouri , David Dos Santos Ferreira , Isabelle Gallagher

We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results…

Analysis of PDEs · Mathematics 2024-07-09 Roman Novikov , Basant Lal Sharma

In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

Analysis of PDEs · Mathematics 2024-12-24 Tianjiao Wang , Xiang Xu , Yue Zhao

We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…

Analysis of PDEs · Mathematics 2021-03-01 Roland Griesmaier , Bastian Harrach

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

Analysis of PDEs · Mathematics 2021-12-08 Xing Cheng , Zhiyuan Li

In this paper, we establish two sharp quantitative results for the direct and inverse time-harmonic acoustic wave scattering. The first one is concerned with the recovery of the support of an inhomogeneous medium, independent of its…

Analysis of PDEs · Mathematics 2022-01-07 Emilia L. K. Blåsten , Hongyu Liu

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

Analysis of PDEs · Mathematics 2023-06-21 Jian Zhai , Yue Zhao

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2020-02-19 Rakesh , Mikko Salo

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…

Analysis of PDEs · Mathematics 2024-10-11 Peijun Li , Ying Liang , Xu Wang

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Numerical Analysis · Mathematics 2016-05-23 Michael V. Klibanov , Hui Liu , Loc H. Nguyen

This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…

Analysis of PDEs · Mathematics 2024-10-15 Peijun Li , Zhenqian Li , Ying Liang

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

Analysis of PDEs · Mathematics 2022-01-04 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar , O. Oukdach