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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

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…

Analysis of PDEs · Mathematics 2020-07-13 Boya Liu

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…

Analysis of PDEs · Mathematics 2012-05-31 Habib Ammari , Hajer Bahouri , David Dos Santos Ferreira , Isabelle Gallagher

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 consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

Analysis of PDEs · Mathematics 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…

Analysis of PDEs · Mathematics 2024-05-01 Boya Liu

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…

Analysis of PDEs · Mathematics 2024-03-14 Ibtissem Ben Aïcha , Guanghui Hu , Suliang Si

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

Analysis of PDEs · Mathematics 2022-01-04 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar , O. Oukdach

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 investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential…

Analysis of PDEs · Mathematics 2024-10-07 Sen Zou , Shuai Lu , Boxi Xu

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

The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…

Analysis of PDEs · Mathematics 2020-03-31 Gang Bao , Faouzi Triki

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a…

Analysis of PDEs · Mathematics 2022-10-12 Lauri Oksanen , Tianyu Yang , Yang Yang

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…

Analysis of PDEs · Mathematics 2024-10-15 Peijun Li , Zhenqian Li , Ying Liang

We investigate recovery of the (Schr\"odinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a H\"older type stability which is a big improvement over a…

Analysis of PDEs · Mathematics 2020-08-19 Victor Isakov , Shuai Lu , Boxi Xu

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
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