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Related papers: An inverse hyperbolic obstacle problem

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We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

We study some hybrid inverse problems associated to BVP's for Schr\"odinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energies. We establish…

Analysis of PDEs · Mathematics 2021-08-23 Mourad Choulli

This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…

Systems and Control · Electrical Eng. & Systems 2026-05-26 Mohamed Camil Belhadjoudja

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…

Analysis of PDEs · Mathematics 2018-01-17 L. Beilina , M. Cristofol , S. Li , M. Yamamoto

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

Analysis of PDEs · Mathematics 2020-01-08 Alexander Beigl , Otmar Scherzer , Jarle Sogn , Walter Zulehner

In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…

Analysis of PDEs · Mathematics 2016-10-06 Antonino Morassi , Edi Rosset

We present an inverse problem which uses the renormalized area functional on minimal submanifolds to recover the expansion of asymptotically hyperbolic, conformally compact metrics which are partially even to high order. We use a rigidity…

Differential Geometry · Mathematics 2024-01-17 Jared Marx-Kuo

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic…

Analysis of PDEs · Mathematics 2017-10-25 Youjun Deng , Hongyu Liu , Gunther Uhlmann

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…

Analysis of PDEs · Mathematics 2021-04-29 Jiaqing Yang

This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…

Optimization and Control · Mathematics 2024-09-17 S. E. Chorfi , L. Maniar

In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…

Optimization and Control · Mathematics 2020-11-30 Jean-Michel Coron , Long Hu , Guillaume Olive , Peipei Shang

There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics. These notes focus on the Boundary Control method, but we will have…

Analysis of PDEs · Mathematics 2026-04-14 Medet Nursultanov , Lauri Oksanen

In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Legendre transform and the implicit function theorem, we prove…

Analysis of PDEs · Mathematics 2016-05-09 Herbert Koch , Angkana Rüland , Wenhui Shi

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

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

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

Analysis of PDEs · Mathematics 2007-12-07 Roman Novikov

We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the…

Mathematical Physics · Physics 2022-07-27 Stefano Marò , Claudio Bonanno

Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a few Dirac masses at unknown locations. Is this information enough to recover the operator and the impulse responses…

Signal Processing · Electrical Eng. & Systems 2021-11-04 Valentin Debarnot , Pierre Weiss

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…

Analysis of PDEs · Mathematics 2021-11-01 G. Yu. Mehdiyeva , Y. T. Mehraliyev , E. I. Azizbayov

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

Analysis of PDEs · Mathematics 2026-03-11 Kuang Huang , Bangti Jin , Yavar Kian , Faouzi Triki