English
Related papers

Related papers: Stability estimate in an inverse problem for non-a…

200 papers

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…

Analysis of PDEs · Mathematics 2018-01-17 L. Beilina , M. Cristofol , S. Li , M. Yamamoto

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

We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…

Analysis of PDEs · Mathematics 2023-02-01 Yavar Kian

This work is composed of two parts. We prove in the first part the uniqueness of the determination of the unbounded zero-order coefficient in a parabolic equation from boundary measurements. The novelty of our result is that it covers the…

Analysis of PDEs · Mathematics 2024-12-16 Mourad Choulli

In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…

Spectral Theory · Mathematics 2024-09-25 Natalia P. Bondarenko

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…

Analysis of PDEs · Mathematics 2016-11-03 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro , Eva Sincich

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

Analysis of PDEs · Mathematics 2024-02-21 Katya Krupchyk , Shiqi Ma , Suman Kumar Sahoo , Mikko Salo , Simon St-Amant

We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…

Analysis of PDEs · Mathematics 2024-10-29 Li Li

A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…

Analysis of PDEs · Mathematics 2015-11-11 Mourad Choulli , Faouzi Triki

We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…

Analysis of PDEs · Mathematics 2020-10-21 X. Huang , A. Kawamoto

In this paper, by constructing the weight functions, a global Carleman estimate for the Schrodinger equation on a tree is established, with a strong assumption on the solution. And the estimate is able to be applied to derive the Lipschitz…

Analysis of PDEs · Mathematics 2023-06-13 Yibin Ding , Xiang Xu

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…

Analysis of PDEs · Mathematics 2025-10-10 Rodrigo Lecaros , Juan López-Ríos , Ariel A. Pérez

We study the impedance boundary map (or Robin-to-Robin map) for the Schrodinger equation in open bounded demain at fixed energy in multidimensions. We give global stability estimates for determining potential from these boundary data and,…

Analysis of PDEs · Mathematics 2013-06-27 Mikhail Isaev , Roman Novikov

We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…

Analysis of PDEs · Mathematics 2017-07-04 Jonathan Di Cosmo , Jean Van Schaftingen

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…

Analysis of PDEs · Mathematics 2018-10-30 Mourad Bellassoued , Mourad Choulli , Dos Santos Ferreira , Yavar Kian , Plamen Stefanov

This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some…

Analysis of PDEs · Mathematics 2011-11-30 Francis J. Chung

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 study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…

Analysis of PDEs · Mathematics 2024-05-01 Boya Liu

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao