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This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Analysis of PDEs · Mathematics 2024-02-09 Yi-Hsuan Lin , Teemu Tyni , Philipp Zimmermann

This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…

Analysis of PDEs · Mathematics 2026-02-24 Peijun Li , Zhenqian Li

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…

Mathematical Physics · Physics 2009-11-11 Alexandre Jollivet

We consider the problem of recovering a smooth, compactly supported potential on R^3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled…

Analysis of PDEs · Mathematics 2015-06-16 Rakesh , Gunther Uhlmann

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

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 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

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…

Numerical Analysis · Mathematics 2017-08-08 Qin Li , Ruiwen Shu , Li Wang

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…

Analysis of PDEs · Mathematics 2021-06-16 Yavar Kian

In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave…

Analysis of PDEs · Mathematics 2019-09-13 Gong Chen

In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…

Analysis of PDEs · Mathematics 2023-05-09 Barbara Kaltenbacher

The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point source identification, mainly due to the inherent solution…

Numerical Analysis · Mathematics 2024-08-20 Tianhao Hu , Bangti Jin , Zhi Zhou

This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian…

Analysis of PDEs · Mathematics 2021-03-23 Jianliang Li , Peijun Li , Xu Wang

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

Analysis of PDEs · Mathematics 2024-06-04 Xiaoxu Xu , Guanghui Hu

We prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time-harmonic Maxwell equations in certain anisotropic settings. We give a uniqueness result in the inverse problem for Maxwell…

Analysis of PDEs · Mathematics 2019-12-19 Carlos E. Kenig , Mikko Salo , Gunther Uhlmann

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Numerical Analysis · Mathematics 2020-08-26 Barbara Kaltenbacher , William Rundell

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm

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

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…

Analysis of PDEs · Mathematics 2015-10-01 Kais Ammari , Mourad Choulli , Faouzi Triki