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In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous justification of increasing stability for the IBVP for Schr\"{o}dinger equation were…

Analysis of PDEs · Mathematics 2023-01-13 Pu-Zhao Kow , Gunther Uhlmann , Jenn-Nan Wang

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

This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…

Analysis of PDEs · Mathematics 2025-12-23 Yang Liu , Yixian Gao

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 the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].

Analysis of PDEs · Mathematics 2011-05-17 Oleg Imanuvilov , Masahiro Yamamoto

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

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…

Analysis of PDEs · Mathematics 2011-10-25 Sei Nagayasu , Gunther Uhlmann , Jenn-Nan Wang

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

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 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 paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…

Analysis of PDEs · Mathematics 2024-02-27 Suliang Si

This paper concerns inverse problems for strongly coupled Schr\"odinger equations. The purpose of this inverse problem is to retrieve a stationary potential in the strongly coupled Schr\"odinger equations from either boundary or internal…

Analysis of PDEs · Mathematics 2020-12-09 Xiaomin Zhu , Fangfang Dou

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

Analysis of PDEs · Mathematics 2024-11-26 Mourad Choulli , Hiroshi Takase

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

In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…

Analysis of PDEs · Mathematics 2018-04-18 Mozhgan Nora Entekhabi , Victor Isakov

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Analysis of PDEs · Mathematics 2016-09-21 Kais Ammari , Mourad Choulli , Faouzi Triki

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…

Analysis of PDEs · Mathematics 2022-11-08 Xiaomeng Zhao , Ganghua Yuan

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

We study increasing stability in the inverse source problems for the Helmholtz equation and the classical Lame system from (minimal) boundary data at multiple wave numbers. By using the Fourier transform with respect to wave numbers,…

Analysis of PDEs · Mathematics 2018-09-03 Mozhgan Nora Entrekhabi , Victor Isakov

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
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