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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

In this note we reprove the Lipschitz stability for the inverse problem for the Schr\"odinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schr\"odinger…

Analysis of PDEs · Mathematics 2020-02-24 Angkana Rüland , Eva Sincich

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

We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

Analysis of PDEs · Mathematics 2018-09-19 Freddy J. F. Symons

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

In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$…

Mathematical Physics · Physics 2013-08-08 Ru-Yu Lai

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 paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely,…

Analysis of PDEs · Mathematics 2015-07-27 Mourad Bellassoued , Yavar Kian , Eric Soccorsi

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…

Analysis of PDEs · Mathematics 2022-04-27 Shuai Lu , Mikko Salo , Boxi Xu

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…

Analysis of PDEs · Mathematics 2025-12-29 Tianjiao Wang , Xiang Xu , Yue Zhao

We obtain H\"older stability estimates for the inverse Steklov and Calder\'on problems for Schr\"odinger operators corresponding to a special class of $L^2$ radial potentials on the unit ball. These results provide an improvement on earlier…

Analysis of PDEs · Mathematics 2023-11-28 Thierry Daudé , Niky Kamran , François Nicoleau

In this article, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of…

Analysis of PDEs · Mathematics 2016-06-29 Youssef Mejri

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

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 derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schr\"odinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when…

Analysis of PDEs · Mathematics 2013-09-12 Victor Isakov , Jenn-Nan Wang

This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…

Analysis of PDEs · Mathematics 2025-05-14 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

In this article we study stability aspects for the determination of time-dependent vector and scalar potentials in relativistic Schr\"odinger equation from partial knowledge of boundary measurements. For space dimensions strictly greater…

Analysis of PDEs · Mathematics 2020-12-30 Soumen Senapati

We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…

Numerical Analysis · Mathematics 2013-07-23 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar

We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…

Optimization and Control · Mathematics 2020-09-15 Ahmet Batal , Türker Özsarı , Kemal Cem Yılmaz