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We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…

Analysis of PDEs · Mathematics 2007-08-17 Matias Dahl , Anna Kirpichnikova , Matti Lassas

We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…

Analysis of PDEs · Mathematics 2012-10-04 Shitao Liu , Lauri Oksanen

In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…

Analysis of PDEs · Mathematics 2017-10-10 Maarten de Hoop , Paul Kepley , Lauri Oksanen

We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…

Analysis of PDEs · Mathematics 2017-02-14 Alexey Agaltsov

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

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2017-02-10 Maarten V. de Hoop , Gen Nakamura , Jian Zhai

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

Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…

Analysis of PDEs · Mathematics 2024-04-24 Thomas Perrin

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

Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a…

Analysis of PDEs · Mathematics 2017-10-10 Maarten V. de Hoop , Paul Kepley , Lauri Oksanen

We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…

Analysis of PDEs · Mathematics 2020-09-03 Tianyu Yang , Yang Yang

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…

Analysis of PDEs · Mathematics 2011-01-26 Lauri Oksanen

We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…

Analysis of PDEs · Mathematics 2017-03-29 Georgi Vodev

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

We consider the inverse problem to determine a smooth compact Riemannian manifold with boundary $(M, g)$ from a restriction $\Lambda_{\Src, \Rec}$ of the Dirichlet-to-Neumann operator for the wave equation on the manifold. Here $\Src$ and…

Analysis of PDEs · Mathematics 2015-01-14 Matti Lassas , Lauri Oksanen

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…

Analysis of PDEs · Mathematics 2022-05-17 Fanghua Lin , Zhongwei Shen

We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…

Mathematical Physics · Physics 2015-06-19 M. I. Belishev , M. N. Demchenko

We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that…

Analysis of PDEs · Mathematics 2016-12-13 Maarten de Hoop , Paul Kepley , Lauri Oksanen

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

This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space.The method constructs the interior Dirichlet-to-Neumann (DtN) map…

Numerical Analysis · Mathematics 2013-08-29 Adrianna Gillman , Alex Barnett , Per-Gunnar Martinsson
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