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We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…

Analysis of PDEs · Mathematics 2022-07-01 Xuezhu Lu

We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the…

Analysis of PDEs · Mathematics 2026-02-10 Yavar Kian , Lauri Oksanen , Ziyao Zhao

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

Using the Observable form of Maxwell's equations, we reveal that effective parameters at materials boundaries emerge naturally as anisotropic transfer functions. The complexity of the boundary dictates the order of these functions.…

Classical Physics · Physics 2024-01-23 Sameh Y. ELnaggar , Yahia. M. Antar

We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…

Analysis of PDEs · Mathematics 2019-03-05 Cătălin I. Cârstea , Gen Nakamura , Lauri Oksanen

We study inverse boundary problems for first order perturbations of the biharmonic operator on a conformally transversally anisotropic Riemannian manifold of dimension $n \ge 3$. We show that a continuous first order perturbation can be…

Analysis of PDEs · Mathematics 2020-12-29 Lili Yan

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

Mathematical Physics · Physics 2013-03-12 Oleg Yu Imanuvilov , M. Yamamoto

We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi , Joonas Ilmavirta , Yavar Kian , Lauri Oksanen

In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\it…

Analysis of PDEs · Mathematics 2016-07-22 Masaru Ikehata

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $\Sigma$ of the…

Analysis of PDEs · Mathematics 2017-12-06 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro

In this paper, we investigate the anisotropic Calder{\'o}n problem on cylindrical Riemannian manifolds with boundary having two ends and equipped with singular metrics of (simple or double) warped product type, that is whose warping factors…

Analysis of PDEs · Mathematics 2018-05-16 Thierry Daude , Niky Kamran , Francois Nicoleau

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

We study the inverse boundary problem for a nonlinear magnetic Schr\"odinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the…

Analysis of PDEs · Mathematics 2023-10-25 Katya Krupchyk , Gunther Uhlmann

We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$…

General Relativity and Quantum Cosmology · Physics 2011-11-14 M. Novello , F. T. Falciano , E. Goulart

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Analysis of PDEs · Mathematics 2026-01-19 Chengyu Wu , Jiaqing Yang

Pride (1994, Phys. Rev. B 50 15678-96) derived the governing model of electroseismic conversion, in which Maxwell's equations are coupled with Biot's equations through an electrokinetic mobility parameter. The inverse problem of…

Analysis of PDEs · Mathematics 2014-06-03 Jie Chen , Maarten de Hoop

In this paper we prove uniqueness in the inverse boundary value problem for quasilinear elliptic equations whose linear part is the Laplacian and nonlinear part is the divergence of a function analytic in the gradient of the solution. The…

Analysis of PDEs · Mathematics 2023-05-10 Cătălin I. Cârstea , Ali Feizmohammadi

We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…

Analysis of PDEs · Mathematics 2018-11-19 Bastian Harrach , Yi-Hsuan Lin , Hongyu Liu