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We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension $n\geq 2$, stability estimates with…

Analysis of PDEs · Mathematics 2019-04-30 Mourad Bellassoued , Ibtissem Ben Aicha

We consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x…

Analysis of PDEs · Mathematics 2016-02-01 Mourad Choulli , Yavar Kian

We consider compact smooth Riemmanian manifolds with boundary of dimension greater than or equal to two. For the initial-boundary value problem for the wave equation with a lower order term $q(t,x)$, we can recover the X-ray transform of…

Analysis of PDEs · Mathematics 2014-08-01 Alden Waters

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha

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 is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary…

Analysis of PDEs · Mathematics 2017-10-11 Mourad Bellassoued , Ibtissem Ben Aïcha

This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold. We show that an unknown potential $q$ in the non-linear wave…

Analysis of PDEs · Mathematics 2025-05-14 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

We give a new stability estimate for the problem of determining the time-dependent zero order coefficient in a parabolic equation from a partial parabolic Dirichlet-to-Neumann map. The novelty of our result is that, contrary to the previous…

Analysis of PDEs · Mathematics 2016-05-30 Mourad Choulli , Yavar Kian

We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that…

Analysis of PDEs · Mathematics 2017-09-13 Ibtissem Ben Aicha

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

We consider the inverse boundary value problem for operators of the form $-\triangle+q$ in an infinite domain $\Omega=\mathbb{R}\times\omega\subset\mathbb{R}^{1+n}$, $n\geq3$, with a periodic potential $q$. For Dirichlet-to-Neumann data…

Analysis of PDEs · Mathematics 2017-11-28 Sombuddha Bhattacharyya , Cătălin I. Cârstea

Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Consider the second order hyperbolic initial-boundary value problem (\delta_t^2 + P(x,D))u = 0 in (0,T) x M, u(0,x) = \delta_t u(0,x) = 0 for x in M, u(t,x) = f(t,x) on…

Analysis of PDEs · Mathematics 2014-10-13 Carlos Montalto

In this paper, we study the stability in the inverse problem of determining the time dependent absorption coefficient appearing in the linear Boltzmann equation, from boundary observations. We prove in dimension $n\geq 2$, that the…

Analysis of PDEs · Mathematics 2019-09-04 Mourad Bellassoued , Yosra Boughanja

In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the…

Analysis of PDEs · Mathematics 2010-05-04 Mourad Bellassoued , David Dos Santos Ferreira

We prove stability for a formally determined inverse problem for a hyperbolic PDE where the coefficients depend on space and time variables. The hyperbolic operator has constant wave speed and we study the recovery of zeroth order and first…

Analysis of PDEs · Mathematics 2021-06-21 Venky Krishnan , Rakesh , Soumen Senapati

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

We consider the inverse problem of determining the time dependent magnetic field of the Schr\"odinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken…

Analysis of PDEs · Mathematics 2012-09-27 Michel Cristofol , Eric Soccorsi

We analyze the stability of an inverse problem for determining the time-dependent matrix potential appearing in the Dirichlet initial-boundary value problem for the wave equation in an unbounded cylindrical waveguide. The observation is…

Analysis of PDEs · Mathematics 2024-09-04 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth
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