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In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This…

Analysis of PDEs · Mathematics 2018-05-02 Mourad Bellassoued , Zouhour Rezig

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

The problem of identifying an obstruction into a fluid duct has several applications, one of them, for example in medicine the presence of Stenosis in coronary vessels is a life threatening disease. In this paper, we formulate a continuous…

Optimization and Control · Mathematics 2022-10-20 Louis Breton , Cristhian Montoya , Pedro González-Casanova , Jesús López Estrada

We present the results on numerical testing of the Boundary Control Method in the sound speed determination for the acoustic equation on semiplane. This method for solving multidimensional inverse problems requires no a priory information…

Geophysics · Physics 2016-09-27 I. B. Ivanov , M. I. Belishev , V. S. Semenov

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

Analysis of PDEs · Mathematics 2024-01-12 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any…

Analysis of PDEs · Mathematics 2026-02-17 Yang Yang

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…

Numerical Analysis · Mathematics 2025-03-25 Roman Chapko , Leonidas Mindrinos

In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…

Analysis of PDEs · Mathematics 2026-02-06 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

We describe a general multiplier method to obtain boundary stabilization of the wave equation by means of a (linear or quasi-linear) Neumann feedback. This also enables us to get Dirichlet boundary control of the wave equation. This method…

Optimization and Control · Mathematics 2009-03-24 Pierre Cornilleau , Jean-Pierre Loheac

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigourous by using systematic way, based on layer potential…

Analysis of PDEs · Mathematics 2020-07-23 Habib Zribi

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

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Numerical Analysis · Mathematics 2015-05-28 Carlos Borges , Leslie Greengard

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…

Analysis of PDEs · Mathematics 2022-12-28 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.

Mathematical Physics · Physics 2009-09-30 Leonid Pestov , Victoria Bolgova , Oksana Kazarina

We are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…

Analysis of PDEs · Mathematics 2024-09-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

The Westervelt equation models the propagation of nonlinear acoustic waves in a regime well-suited for applications such as medical ultrasound imaging. In this work, we prove that the nonlinear parameter, as well as the sound speed, can be…

Analysis of PDEs · Mathematics 2025-10-06 Mike Wendels

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…

Mathematical Physics · Physics 2012-02-23 M. P. Ramirez T. , C. M. A. Robles G. , R. A. Hernandez-Becerril

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

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Analysis of PDEs · Mathematics 2025-11-27 Xiaoxu Xu , Guanghui Hu

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Analysis of PDEs · Mathematics 2020-09-23 Anna Kirpichnikova , Jussi Korpela , Matti Lassas , Lauri Oksanen