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We study the inverse problem of determining a real-valued potential in the two-dimensional Schr\"odinger equation at negative energy from the Dirichlet-to-Neumann map. It is known that the problem is ill-posed and a stability estimate of…

Analysis of PDEs · Mathematics 2014-02-07 Matteo Santacesaria

We consider an inverse transport problem in fluorescence ultrasound modulated optical tomography (fUMOT) with angularly averaged illuminations and measurements. We study the uniqueness and stability of the reconstruction of the absorption…

Mathematical Physics · Physics 2020-02-19 Wei Li , Yang Yang , Yimin Zhong

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…

Analysis of PDEs · Mathematics 2015-05-14 Guillaume Bal , Gunther Uhlmann

The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…

Spectral Theory · Mathematics 2020-08-18 Sergey Buterin

We consider a second-order hyperbolic equation on an open bounded domain $\Omega$ in $\mathbb{R}^n$ for $n\geq2$, with $C^2$-boundary $\Gamma=\pa\Omega=\bar{\Gamma_0\cup\Gamma_1}$, $\Gamma_0\cap\Gamma_1=\emptyset$, subject to…

Analysis of PDEs · Mathematics 2010-10-26 Shitao Liu , Roberto Triggiani

The image restoration problem is one of the popular topics in image processing studied by many authors on account of its applications in various areas. The aim of this paper is to present a new algorithm by using viscosity approximation…

Functional Analysis · Mathematics 2021-08-12 Ebru ALTIPARMAK , Ibrahim KARAHAN

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

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

The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…

Numerical Analysis · Mathematics 2022-01-06 Zhengqi Zhang , Zhidong Zhang , Zhi Zhou

In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…

Numerical Analysis · Mathematics 2022-09-23 Bangti Jin , Zhi Zhou

In photoacoustic imaging the objective is to determine the optical properties of biological tissue from boundary measurement of the generated acoustic wave. Here, we propose a restriction to piecewise constant media parameters. Precisely we…

Analysis of PDEs · Mathematics 2024-07-09 Yavar Kian , Faouzi Triki

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…

Analysis of PDEs · Mathematics 2018-09-20 Henrik Garde , Stratos Staboulis

We consider the recovery of a potential associated with a semi-linear wave equation on $\mathbb{R}^{n+1}$, $n\geq 1$. We show a H\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\square u +a…

Analysis of PDEs · Mathematics 2020-06-24 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…

Analysis of PDEs · Mathematics 2021-12-22 Yavar Kian , Eric Soccorsi , Faouzi Triki

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…

Analysis of PDEs · Mathematics 2023-02-07 Li Li

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

Numerical Analysis · Mathematics 2025-08-22 Tianhao Hu , Xinchi Huang , Bangti Jin , Qimeng Quan , Zhi Zhou

This work considers the time-domain fluorescence diffuse optical tomography (FDOT). We recover the distribution of fluorophores in biological tissue by the boundary measurements. With the Laplace transform and the knowledge of complex…

Analysis of PDEs · Mathematics 2022-09-14 Chunlong Sun , Zhidong Zhang

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a…

Analysis of PDEs · Mathematics 2022-10-12 Lauri Oksanen , Tianyu Yang , Yang Yang

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary…

Analysis of PDEs · Mathematics 2017-10-11 Mourad Bellassoued , Ibtissem Ben Aïcha
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