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We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

Analysis of PDEs · Mathematics 2021-12-08 Xing Cheng , Zhiyuan Li

In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…

Analysis of PDEs · Mathematics 2024-11-08 Suliang Si

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

Analysis of PDEs · Mathematics 2016-09-27 Francis J Chung , John C Schotland

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Analysis of PDEs · Mathematics 2020-04-21 Giovanni S. Alberti , Matteo Santacesaria

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability…

Analysis of PDEs · Mathematics 2021-05-06 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar

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 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

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

We study an inverse scattering problem of a perturbed biharmonic operator. we show that the high-frequency asymptotic of scattering amplitude of the biharmonic operator uniquely determine the curl A and {V -1/2 nablaA}. We also study the…

Analysis of PDEs · Mathematics 2019-11-21 Siamak RabieniaHaratbar

We prove new global H\"older-logarithmic stability estimates for the near-field inverse scattering problem in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently…

Analysis of PDEs · Mathematics 2013-06-27 Mikhail Isaev

In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…

Analysis of PDEs · Mathematics 2021-02-10 Peijun Li , Xiaohua Yao , Yue Zhao

Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…

Numerical Analysis · Mathematics 2025-11-25 Mahadevan Ganesh , Stuart C. Hawkins , Darko Volkov

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…

Analysis of PDEs · Mathematics 2023-02-01 Yavar Kian

In this paper we establish a global Carleman estimate for the fourth order Schr\"odinger equation posed on a $1-d$ finite domain. The Carleman estimate is used to prove the Lipschitz stability for an inverse problem consisting in retrieving…

Analysis of PDEs · Mathematics 2013-12-18 Chuang Zheng

In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…

Analysis of PDEs · Mathematics 2014-07-03 Sergio Vessella

We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…

Analysis of PDEs · Mathematics 2019-07-24 Faouzi Triki , Darko Volkov