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We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave…

Analysis of PDEs · Mathematics 2022-03-17 Sombuddha Bhattacharyya , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

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 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

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Spectral Theory · Mathematics 2012-05-22 Jussi Behrndt , Jonathan Rohleder

The paper deals with the inverse problem of determining a polyhedral inclusion compactly contained in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and…

Analysis of PDEs · Mathematics 2025-08-11 Andrea Aspri , Elena Beretta , Elisa Francini , Antonino Morassi , Edi Rosset , Eva Sincich , Sergio Vessella

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schr{\"o}dinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data…

Analysis of PDEs · Mathematics 2015-01-09 Mourad Choulli , Yavar Kian , Eric Soccorsi

We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…

Optimization and Control · Mathematics 2025-05-29 Houcine Meftahi , Chayma Nssibi

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

In this paper, we consider the inverse boundary value problem for the polyharmonic operator. We prove that the second order perturbations are uniquely determined by the corresponding Dirichlet to Neumann map. More precisely, we show in…

Analysis of PDEs · Mathematics 2022-09-27 Nesrine Aroua , Mourad Bellassoued

We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and let \(R(p)\) be the finite-dimensional quantity to be…

Analysis of PDEs · Mathematics 2026-05-08 Cătălin I. Cârstea

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet-to-Neumann map. We extend here the stability result obtained by Alessandrini and…

Analysis of PDEs · Mathematics 2016-11-04 Romina Gaburro , Eva Sincich

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Analysis of PDEs · Mathematics 2022-03-18 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…

Numerical Analysis · Mathematics 2021-08-02 Elie Bretin , Pierre Millien , Laurent Seppecher

We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map…

Analysis of PDEs · Mathematics 2020-12-08 Yi-Hsuan Lin

We investigate the inverse problem of determining nonlinear elastic material parameters from boundary stress measurements corresponding to prescribed boundary displacements. The material law is described by a nonlinear, space-independent…

Analysis of PDEs · Mathematics 2026-01-23 David Johansson , Yavar Kian

In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the…

Analysis of PDEs · Mathematics 2010-05-04 Mourad Bellassoued , David Dos Santos Ferreira

We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…

Numerical Analysis · Mathematics 2017-06-08 Stefan Kindermann

We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…

Analysis of PDEs · Mathematics 2021-09-01 Darko Volkov , Yulong Jiang

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

Analysis of PDEs · Mathematics 2016-01-21 Mourad Choulli , Yavar Kian , Eric Soccorsi