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Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…

Analysis of PDEs · Mathematics 2025-05-06 Hany Gerges , Jaan Janno

This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…

Analysis of PDEs · Mathematics 2020-02-19 Deyue Zhang , Yinglin Wang , Yukun Guo , Jingzhi Li

A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…

Numerical Analysis · Mathematics 2008-09-24 Hua Shan , M. V. Klibanov , Jianzhong Su , Natee Pantong , Hanli Liu

This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we…

Numerical Analysis · Mathematics 2026-04-28 Guanqiu Ma , Hongxia Guo , Guanghui Hu

We extend the recent study of inverse problems for minimal surfaces by considering the inverse source problem for the prescribed mean curvature equation \begin{equation*} \nabla \cdot \left[ \frac{\nabla u}{(1 + |\nabla u|^2)^{1/2}} \right]…

Analysis of PDEs · Mathematics 2026-02-06 Tony Liimatainen , Janne Nurminen

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…

Numerical Analysis · Mathematics 2021-01-14 Xiaoli Feng , Meixia Zhao , Peijun Li , Xu Wang

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…

Analysis of PDEs · Mathematics 2016-08-25 Zhiyuan Li

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…

Optimization and Control · Mathematics 2022-09-28 William W. Symes

We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard…

Analysis of PDEs · Mathematics 2015-06-11 Lauri Oksanen

This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…

Analysis of PDEs · Mathematics 2022-06-22 Barbara Kaltenbacher , William Rundell

This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…

Analysis of PDEs · Mathematics 2026-03-03 Ravshan Ashurov , Damir Shamuratov

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

Numerical Analysis · Mathematics 2025-11-04 Hao Gu , Tianjiao Wang , Xiang Xu , Yue Zhao

In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic…

Analysis of PDEs · Mathematics 2025-09-16 Cătălin I. Cârstea , Ali Feizmohammadi

We consider the subsonic moving point source problem for the scalar wave equation in $\pmb{R}^3$, proving a regularity result for the direct problem, and uniqueness and stability results for the inverse problem. We then present and…

Analysis of PDEs · Mathematics 2022-04-12 Sára Wang , Mirza Karamehmedović , Faouzi Triki

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…

Analysis of PDEs · Mathematics 2022-10-11 Shitao Liu , Antonio Pierrottet , Scott Scruggs

This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…

Analysis of PDEs · Mathematics 2020-04-08 Elham Sohrabi

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

We study the reconstruction of the initial pressure $f(x)=p(x,0)$ for the wave model \[ \partial_t^2 p(x,t)=c(x)\Delta_{x}p(x,t)\qquad (x,t)\in\Omega\times[0,\infty), \] posed on a bounded domain $\Omega$ with variable sound speed…

Analysis of PDEs · Mathematics 2026-04-29 Sunghwan Moon , Ihyeok Seo

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li