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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 consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…

Numerical Analysis · Mathematics 2025-10-24 Erik Burman , Lauri Oksanen , Janosch Preuss , Ziyao Zhao

We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…

Numerical Analysis · Mathematics 2014-10-24 S. O. Hussein , D. Lesnic

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

Analysis of PDEs · Mathematics 2023-04-06 Pu-Zhao Kow , Yi-Hsuan Lin , Jenn-Nan Wang

We prove a logarithmic stability estimate for the time dependent X-ray transform on $\mathbb{R}_t^+\times\mathbb{R}^n$. To do so, we extend a known result by Begmatov for the stability of the time dependent X-ray transform in…

Analysis of PDEs · Mathematics 2015-10-02 Alden Waters

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

Analysis of PDEs · Mathematics 2023-01-20 Bochao Chen , Yixian Gao , Shuguan Ji , Yang Liu

For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish H\"older type stability estimates in the geometric inverse problem of determining the electric…

Analysis of PDEs · Mathematics 2022-07-19 Victor Arnaiz , Colin Guillarmou

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 investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

Analysis of PDEs · Mathematics 2026-04-15 Irina Kmit , Nataliya Protsakh , Viktor Tkachenko

In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2020-12-07 Gen Nakamura , Manmohan Vashisth , Michiyuki Watanabe

In this paper, we consider the inverse boundary value problem for the polyharmonic operator. We prove that the second order perturbations are uniquely determined by the corresponding Dirichlet to Neumann map. More precisely, we show in…

Analysis of PDEs · Mathematics 2022-09-27 Nesrine Aroua , Mourad Bellassoued

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

Analysis of PDEs · Mathematics 2016-02-01 Otared Kavian , Yavar Kian , Eric Soccorsi

This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

Analysis of PDEs · Mathematics 2024-08-01 Adel Blouza , Léo Glangetas , Yavar Kian , Van-Sang Ngo

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

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 paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…

Numerical Analysis · Mathematics 2021-01-19 Olaf Steinbach , Marco Zank

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , V. S. Mikhaylov

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…

Analysis of PDEs · Mathematics 2016-08-25 Zhiyuan Li

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…

Optimization and Control · Mathematics 2018-05-09 Antonio Agresti , Daniele Andreucci , Paola Loreti