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An inverse boundary value problem for a 1+1 dimensional wave equation with wave speed $c(x)$ is considered. We give a regularisation strategy for inverting the map $\mathcal A:c\mapsto \Lambda,$ where $\Lambda$ is the hyperbolic…

Analysis of PDEs · Mathematics 2016-05-04 Jussi Korpela , Matti Lassas , Lauri Oksanen

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet-to-Neumann map. We extend here the stability result obtained by Alessandrini and…

Analysis of PDEs · Mathematics 2016-11-04 Romina Gaburro , Eva Sincich

In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity…

Numerical Analysis · Mathematics 2018-10-29 Erik Burman , Mihai Nechita , Lauri Oksanen

In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…

Numerical Analysis · Mathematics 2019-04-08 Bastian Harrach , Houcine Meftahi

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

Analysis of PDEs · Mathematics 2016-01-21 Mourad Choulli , Yavar Kian , Eric Soccorsi

The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction…

Analysis of PDEs · Mathematics 2013-06-28 Matteo Santacesaria

In this paper we consider the problem of recovering the conformal factor in a conformal class of Riemannian metrics from the boundary measurement of one wave field. More precisely, using boundary control operators, we derive an explicit…

Analysis of PDEs · Mathematics 2015-03-30 Sebastian Acosta

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…

Analysis of PDEs · Mathematics 2017-05-12 Kiril Datchev , Maarten V. de Hoop

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

Numerical Analysis · Mathematics 2018-06-19 Ramaz Botchorishvili , Tamar Janelidze

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Analysis of PDEs · Mathematics 2022-03-18 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

Analysis of PDEs · Mathematics 2021-12-08 Xing Cheng , Zhiyuan Li

This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Analysis of PDEs · Mathematics 2024-02-09 Yi-Hsuan Lin , Teemu Tyni , Philipp Zimmermann

Inverse nodal problem on Dirac operator is finding the parameters in the boundary conditions, the number m and the potential function V in the Dirac equations by using a set of nodal points of a component of two component vector…

Spectral Theory · Mathematics 2020-03-02 Emrah Yilmaz , Hikmet Kemaloglu

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 linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…

Analysis of PDEs · Mathematics 2024-10-15 Türker Özsarı , İdem Susuzlu

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…

Analysis of PDEs · Mathematics 2025-10-10 Rodrigo Lecaros , Juan López-Ríos , Ariel A. Pérez

We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…

Analysis of PDEs · Mathematics 2020-09-10 Manabu Machida , Masahiro Yamamoto

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

Analysis of PDEs · Mathematics 2015-10-19 Vo Anh Khoa

In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…

Analysis of PDEs · Mathematics 2026-05-13 Bin Wu , Xu Zhu , Wenwen Zhou , Zewen Wang

The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the…

Analysis of PDEs · Mathematics 2021-09-01 Gang Bao , Yuantong Liu , Faouzi Triki
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