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We consider the problem of recovering a nonlinear potential function in a nonlinear Schr\"odinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex…

Analysis of PDEs · Mathematics 2023-01-20 Shuai Lu , Jian Zhai

In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary…

Analysis of PDEs · Mathematics 2017-11-15 Anupam Pal Choudhury , Horst Heck

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…

Analysis of PDEs · Mathematics 2015-05-04 Ru-Yu Lai , Victor Isakov , Jenn-Nan Wang

We study the stability issue for the inverse problem of determining a coefficient appearing in a Schr\"odinger equation defined on an infinite cylindrical waveguide. More precisely, we prove the stable recovery of some general class of…

Analysis of PDEs · Mathematics 2021-03-22 Yosra Soussi

We study the inverse problem of determining a real-valued potential in the two-dimensional Schr\"odinger equation at negative energy from the Dirichlet-to-Neumann map. It is known that the problem is ill-posed and a stability estimate of…

Analysis of PDEs · Mathematics 2014-02-07 Matteo Santacesaria

We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…

Analysis of PDEs · Mathematics 2025-01-23 Mourad Choulli

We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that…

Analysis of PDEs · Mathematics 2017-09-13 Ibtissem Ben Aicha

In this paper we are interested in establishing stability estimates in the inverse problem of determining on a compact Riemannian manifold the electric potential or the conformal factor in a Schr\"odinger equation with Dirichlet data from…

Analysis of PDEs · Mathematics 2015-05-19 Mourad Bellassoued , David Dos Santos Ferreira

The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction…

Analysis of PDEs · Mathematics 2013-06-28 Matteo Santacesaria

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

Analysis of PDEs · Mathematics 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

We show that potentials with jump discontinuities can be recovered from the Dirichlet-to-Neumann map using Bukhgeim's method. Combining with known formulas, this enables the recovery from the scattering amplitude at a fixed energy. We also…

Analysis of PDEs · Mathematics 2016-07-18 Jorge Tejero

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

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

Analysis of PDEs · Mathematics 2013-02-06 V Isakov , S Nagayasu , G Uhlmann , J-N Wang

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 consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded…

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

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

Analysis of PDEs · Mathematics 2023-06-21 Jian Zhai , Yue Zhao

We relax the regularity condition on potentials of Schr\"odinger equations in the uniqueness results in \cite{EB} and \cite{IY2} for the inverse boundary value problem of determining a potential by Dirichlet-to-Neumann map.

Mathematical Physics · Physics 2012-08-21 Oleg Yu. Imanuvilov , Masahiro Yamamoto

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

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…

Analysis of PDEs · Mathematics 2021-10-19 Anupam Pal Choudhury , Venkateswaran P. Krishnan
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