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This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…

Numerical Analysis · Mathematics 2017-02-09 Frederic Weidling , Thorsten Hohage

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

In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies…

Analysis of PDEs · Mathematics 2025-06-17 Suliang Si

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…

Numerical Analysis · Mathematics 2026-03-11 Fenglin Sun , Hongxia Guo

In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…

Analysis of PDEs · Mathematics 2020-12-30 X. Huang , O. Yu. Imanuvilov , M. Yamamoto

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…

Numerical Analysis · Mathematics 2023-12-21 Eric Lindström , Larisa Beilina

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

Analysis of PDEs · Mathematics 2017-09-13 Yue Zhao , Peijun Li

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 investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Yikan Liu , Masahiro Yamamoto

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…

Analysis of PDEs · Mathematics 2022-08-23 Venkateswaran P. Krishnan , Rakesh , Soumen Senapati

In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.

Analysis of PDEs · Mathematics 2010-05-27 Pedro Caro

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…

Analysis of PDEs · Mathematics 2021-09-01 Gang Bao , Yuantong Liu , Faouzi Triki

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

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $\mathbf{E}_0$ in a bounded domain $\Omega \subset \mathbb{R}^3$, using…

Numerical Analysis · Mathematics 2025-06-27 Thuy T. Le , Cong B. Van , Trong D. Dang , Loc H. Nguyen

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

Analysis of PDEs · Mathematics 2013-02-06 V Isakov , S Nagayasu , G Uhlmann , J-N Wang

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

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

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