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This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

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

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

Numerical Analysis · Mathematics 2016-05-23 Michael V. Klibanov , Hui Liu , Loc H. Nguyen

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

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…

Analysis of PDEs · Mathematics 2023-01-20 Yixian Gao , Hongyu Liu , Yang Liu

In this paper we consider the mathematical model of thermo- and photo-acoustic tomography for the recovery of the initial condition of a wave field from knowledge of its boundary values. Unlike the free-space setting, we consider the wave…

Analysis of PDEs · Mathematics 2015-06-11 Sebastian Acosta , Carlos Montalto

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

Analysis of PDEs · Mathematics 2023-04-25 Xiaomeng Zhao , Ganghua Yuan

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping…

Numerical Analysis · Mathematics 2020-11-17 Gaurav Mittal , Ankik Kumar Giri

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…

Analysis of PDEs · Mathematics 2011-10-24 Guillaume Bal

Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector…

Spectral Theory · Mathematics 2020-03-02 Emrah Yilmaz , Hikmet Kemaloglu

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

Numerical Analysis · Mathematics 2026-03-10 Long-Ling Du , Zejun Sun , Li-Li Wang , Guang-Hui Zheng

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Numerical Analysis · Mathematics 2025-07-11 Yunqing Huang , Shihan Zhang

We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We…

Analysis of PDEs · Mathematics 2017-05-09 Masaru Ikehata

We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy…

Numerical Analysis · Mathematics 2021-07-23 Siddhartha Mishra , David Ochsner , Adrian M. Ruf , Franziska Weber

We study boundary regularity for the inhomogeneous Dirichlet problem for $2s$-stable operators in generalized H\"older spaces. Moreover, we provide explicit counterexamples that showcase the sharpness of our results. Our approach directly…

Analysis of PDEs · Mathematics 2025-10-02 Florian Grube

This paper deals with the Sturm-Liouville problem with singular potential of the Sobolev space $W_2^{-1}$ and polynomials of the spectral parameter in a boundary condition. We prove the uniform boundedness and the uniform stability for the…

Spectral Theory · Mathematics 2025-04-08 N. P. Bondarenko , E. E. Chitorkin

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain from one boundary Neumann observation of the solution. We prove H\"older stability…

Analysis of PDEs · Mathematics 2013-11-22 Yavar Kian , Quang Sang Phan , Eric Soccorsi

We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…

Analysis of PDEs · Mathematics 2022-03-03 Mourad Bellassoued , Houssem Haddar , Amal Labidi

Assume that $M$ is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. Assume we are given, with some error, the first eigenvalues of the Laplacian $\Delta_g$ on…

Analysis of PDEs · Mathematics 2020-01-01 Roberta Bosi , Yaroslav Kurylev , Matti Lassas