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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

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

We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…

Computer Vision and Pattern Recognition · Computer Science 2026-02-11 Joe-Mei Feng , Hsin-Hsiung Kao

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 in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…

Analysis of PDEs · Mathematics 2019-07-24 Faouzi Triki , Darko Volkov

We prove a global H\"older stability estimate for a hybrid inverse problem combining microwave imaging and ultrasound. The principal features of this result are that we assume to have access to measurements associated to a single, arbitrary…

Analysis of PDEs · Mathematics 2015-06-19 Giovanni Alessandrini

We consider the inverse problem of determining the time dependent magnetic field of the Schr\"odinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken…

Analysis of PDEs · Mathematics 2012-09-27 Michel Cristofol , Eric Soccorsi

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

We consider the inverse boundary value problem of determining the potential $q$ in the equation $\Delta u + qu = 0$ in $\Omega\subset\mathbb{R}^n$, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension…

Analysis of PDEs · Mathematics 2017-02-15 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro , Eva Sincich

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…

Analysis of PDEs · Mathematics 2024-02-27 Suliang Si

In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…

Numerical Analysis · Mathematics 2026-01-14 Erik Burman , Janosch Preuss , Tim van Beeck

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

Analysis of PDEs · Mathematics 2015-05-28 Kais Ammari , Mourad Choulli

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…

Analysis of PDEs · Mathematics 2016-12-26 Yavar Kian , Diomba Sambou , Eric Soccorsi

We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz…

Analysis of PDEs · Mathematics 2021-03-23 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…

Analysis of PDEs · Mathematics 2013-09-11 Anne-Claire Egloffe

For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…

Analysis of PDEs · Mathematics 2021-07-12 O. Y. Imanuvilov , M. Yamamoto

A 3D coefficient inverse problem for a hyperbolic equation with non-overdetermined data is considered. The forward problem is the Cauchy problems with the initial condition the delta function concentrated at a single plane (i.e. the plane…

Analysis of PDEs · Mathematics 2022-03-23 Michael V. Klibanov , Vladimir G. Romanov

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