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Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang

In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…

Analysis of PDEs · Mathematics 2014-07-03 Sergio Vessella

We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lam\'e system from near-field measurements.…

Numerical Analysis · Mathematics 2021-11-24 Xianchao Wang , Yukun Guo , Sara Bousba

In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…

Analysis of PDEs · Mathematics 2023-06-28 Matti Lassas , Zhiyuan Li , Zhidong Zhang

We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…

Analysis of PDEs · Mathematics 2018-06-19 Gunther Uhlmann , Yiran Wang

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…

Analysis of PDEs · Mathematics 2024-11-08 Suliang Si

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 study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Analysis of PDEs · Mathematics 2023-05-16 Hongyu Liu , Shiqi Ma

In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…

Analysis of PDEs · Mathematics 2019-03-15 Michael Hinze , Bernd Hofmann , Tran Nhan Tam Quyen

This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…

Analysis of PDEs · Mathematics 2025-09-22 Xu Wang , Guanlin Yang , Zhidong Zhang

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

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

In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…

Analysis of PDEs · Mathematics 2026-02-06 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…

Numerical Analysis · Mathematics 2025-03-11 Xiaodong Liu , Qingxiang Shi

In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…

Analysis of PDEs · Mathematics 2026-05-13 Bin Wu , Xu Zhu , Wenwen Zhou , Zewen Wang

This paper is concerned with inverse source problems for the time-dependent Lam\'e system in an unbounded domain corresponding to the exterior of a bounded cavity or the full space $\R^3$. If the time and spatial variables of the source…

Analysis of PDEs · Mathematics 2019-07-04 Guanghui Hu , Yavar Kian

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

In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…

Analysis of PDEs · Mathematics 2025-08-19 Dian Feng , Yikan Liu , Shuai Lu

We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…

Numerical Analysis · Mathematics 2021-01-12 Thuy T. Le , Loc H. Nguyen , Thi-Phong Nguyen , William Powell