English
Related papers

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

200 papers

We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…

Analysis of PDEs · Mathematics 2018-10-10 Sombuddha Bhattacharyya

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 paper, we study an inverse coefficients problem for two coupled Schr\"{o}dinger equations with an observation of one component of the solution. The observation is done in a nonempty open subset of the domain where the equations…

Analysis of PDEs · Mathematics 2019-07-24 Fangfang Dou , Masahiro Yamamoto

We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger equation. That is in presence of a magnetic potential. We establish…

Analysis of PDEs · Mathematics 2019-09-04 Kaïs Ammari , Mourad Choulli , Luc Robbiano

We give a new stability estimate for the problem of determining the time-dependent zero order coefficient in a parabolic equation from a partial parabolic Dirichlet-to-Neumann map. The novelty of our result is that, contrary to the previous…

Analysis of PDEs · Mathematics 2016-05-30 Mourad Choulli , Yavar Kian

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

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…

Analysis of PDEs · Mathematics 2024-10-11 Peijun Li , Ying Liang , Xu Wang

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

We establish in dimension $3$ a stability inequality for the problem of determining the potential in the Schr\"odinger equation from boundary measurements in the case where the potential belongs to $L^s$ with $s\in (2,3)$.

Analysis of PDEs · Mathematics 2023-10-27 Mourad Choulli

We prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…

Analysis of PDEs · Mathematics 2019-10-10 Giovanni S. Alberti , Matteo Santacesaria

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

We consider the initial-value problem for the Chern-Simons-Schr\"odinger system, which is a gauge-covariant Schr\"{o}dinger system in $\mathbb{R}_t\times\mathbb{R}^2_x$ with a long-range electromagnetic field. We show that, in the Coulomb…

Analysis of PDEs · Mathematics 2016-09-07 Zhuo Min Lim

We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…

Analysis of PDEs · Mathematics 2007-05-23 J. Ginibre , G. Velo

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 paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…

Analysis of PDEs · Mathematics 2023-05-16 Hongyu Liu , Shiqi Ma

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu

We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…

Analysis of PDEs · Mathematics 2025-11-14 Mourad Choulli , Shuai Lu , Hiroshi Takase

We study the stability of the one electron atom Schr\"odinger model with self-generated magnetic field in two dimensions. The magnetic energy is taken of the general form $K\int_{\mathbb{R}^2} |B|^p$ and we study the stability of the model…

Mathematical Physics · Physics 2023-10-23 Ayoub Arraji , Saad Benjelloun , Salma Lahbabi

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

We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…

Analysis of PDEs · Mathematics 2023-09-08 Ru-Yu Lai , Lili Yan
‹ Prev 1 4 5 6 7 8 10 Next ›