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We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…

Analysis of PDEs · Mathematics 2017-06-28 Pedro Caro , Andoni Garcia

The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…

Analysis of PDEs · Mathematics 2026-01-06 Philipp Zimmermann

We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard…

Analysis of PDEs · Mathematics 2015-06-11 Lauri Oksanen

This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…

Analysis of PDEs · Mathematics 2019-02-20 Guanghui Hu , Long Li , Jun Zou

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions…

Differential Geometry · Mathematics 2018-03-20 Matti Lassas , Teemu Saksala , Hanming Zhou

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

Analysis of PDEs · Mathematics 2024-06-18 Ali Feizmohammadi , Yavar Kian , Lauri Oksanen

In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated…

Analysis of PDEs · Mathematics 2022-03-18 Cătălin I. Cârstea , Matti Lassas , Tony Liimatainen , Lauri Oksanen

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

Analysis of PDEs · Mathematics 2025-09-24 A. S. Mikhaylov , V. S. Mikhaylov

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…

Analysis of PDEs · Mathematics 2011-10-21 Lucie Baudouin , Sylvain Ervedoza

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 consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map…

Analysis of PDEs · Mathematics 2016-03-15 Chang-Yu Guo , Manas Kar , Mikko Salo

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

We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a…

Analysis of PDEs · Mathematics 2025-11-13 Boya Liu , Weinan Wang

We study the boundary rigidity problem for compact Riemannian manifolds with boundary $(M,g)$: is the Riemannian metric $g$ uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function $\rho_g(x,y)$…

Differential Geometry · Mathematics 2007-05-23 Plamen Stefanov , Gunther Uhlmann

We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and…

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Spectral Theory · Mathematics 2012-05-22 Jussi Behrndt , Jonathan Rohleder

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

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…

Numerical Analysis · Mathematics 2023-07-06 Yan Chang , Yukun Guo , Tao Yin , Yue Zhao

After giving a general introduction to the main known results on the anisotropic Calder{\'o}n problem on n-dimensional compact Riemannian manifolds with boundary, we give a motivated review of some recent non-uniqueness results obtained in…

Analysis of PDEs · Mathematics 2018-03-05 Thierry Daudé , Niky Kamran , François Nicoleau
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