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In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lam\'e parameters with certain regularity assumptions. In…

Numerical Analysis · Mathematics 2022-12-13 Sarah Eberle , Bastian Harrach , Houcine Meftahi , Taher Rezgui

In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…

Optimization and Control · Mathematics 2025-05-09 Houcine Meftahi , Chayma Nssibi

In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…

Numerical Analysis · Mathematics 2019-04-08 Bastian Harrach , Houcine Meftahi

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

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

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

Analysis of PDEs · Mathematics 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

Analysis of PDEs · Mathematics 2016-09-27 Francis J Chung , John C Schotland

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

Numerical Analysis · Mathematics 2026-01-27 Manabu Machida , Hirofumi Notsu , Julius Fergy Tiongson Rabago

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

Analysis of PDEs · Mathematics 2022-01-04 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar , O. Oukdach

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

This work considers the reconstruction of a space-dependent potential from boundary observations in subdiffusion by a stable and robust recovery method. Specifically, we develop an algorithm to minimize the Kohn-Vogelius cost function,…

Numerical Analysis · Mathematics 2025-10-01 Hamza Kahlaoui , Mourad Hrizi , Abdessamad Oulmelk , Xiangcheng Zheng , Mahmoud A. Zaky , Ahmed Hendy

This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a…

Analysis of PDEs · Mathematics 2012-09-20 Lucie Baudouin , Eduardo Cerpa , Emmanuelle Crépeau , Alberto Mercado

In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse…

Numerical Analysis · Mathematics 2020-09-09 Bangti Jin , Zhi Zhou

We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $\Omega$…

Analysis of PDEs · Mathematics 2020-05-11 Olga Doeva , Romina Gaburro , William R. B. Lionheart , Clifford J. Nolan

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…

Analysis of PDEs · Mathematics 2021-11-10 Giovanni S. Alberti , Matteo Santacesaria

This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…

Numerical Analysis · Mathematics 2024-05-14 Chunlong Sun , Mengmeng Zhang , Zhidong Zhang

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu
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