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This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state…

Numerical Analysis · Mathematics 2025-10-17 Galina García , Joaquín Vidal , Sebastián Zamorano

In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the…

Analysis of PDEs · Mathematics 2023-06-09 Daurenbek Serikbaev , Michael Ruzhansky , Niyaz Tokmagambetov

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

Functional Analysis · Mathematics 2025-01-06 Giovanni S. Alberti , Alessandro Felisi , Matteo Santacesaria , S. Ivan Trapasso

We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…

Numerical Analysis · Mathematics 2023-07-19 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…

Analysis of PDEs · Mathematics 2024-05-24 Azizbek Mamanazarov , Durvudkhan Suragan

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

Numerical Analysis · Mathematics 2025-04-22 Lingyun Qiu , Jiwoon Sim

Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies to make hypotheses on the solution itself, namely…

Solar and Stellar Astrophysics · Physics 2015-05-30 E. Simonneau , O. Cardona , L. Crivellari

We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data…

Exactly Solvable and Integrable Systems · Physics 2024-11-28 Dongli Luan , Bo Xue , Huan Liu

This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The…

Numerical Analysis · Mathematics 2025-07-22 Minghui Li , Guanghui Hu , Yue Zhao

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

Mathematical Physics · Physics 2011-11-10 Ole Henrik Waagaard , Johannes Skaar

In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…

Probability · Mathematics 2016-11-29 Tuan Nguyen Huy , Erkan Nane

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 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 atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…

Statistical Mechanics · Physics 2009-11-11 Michael J. Caola

We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…

Analysis of PDEs · Mathematics 2020-04-17 Mtthias Eller , Philip Hoskins , Leonid Kunyansky

We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…

Numerical Analysis · Mathematics 2017-06-07 Dinh-Liem Nguyen , Michael V. Klibanov , Loc H. Nguyen , Aleksandr E. Kolesov , Michael A. Fiddy , Hui Liu

A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…

Mathematical Physics · Physics 2007-05-23 Tuncay Aktosun , Vassilis G. Papanicolaou , Vassilis Zisis

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

Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…

Numerical Analysis · Mathematics 2022-10-17 Bangti Jin , Yavar Kian , Zhi Zhou

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li