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We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…

Numerical Analysis · Mathematics 2016-01-26 Larisa Beilina , Samar Hosseinzadegan

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

Numerical Analysis · Mathematics 2017-04-10 Andreas Hauptmann , Matteo Santacesaria , Samuli Siltanen

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…

Analysis of PDEs · Mathematics 2013-03-01 Valter Pohjola

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…

Analysis of PDEs · Mathematics 2015-05-14 Guillaume Bal , Gunther Uhlmann

This paper investigates the inverse problem of determining a general Signorini obstacle using boundary measurements. We demonstrate that both the shape of the obstacle and the obstacle function can be uniquely determined from solution…

Analysis of PDEs · Mathematics 2026-05-15 Ziyao Zhao

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

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission…

Analysis of PDEs · Mathematics 2015-06-02 Fioralba Cakoni , Houssem Haddar , Shixu Meng

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

This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of…

Analysis of PDEs · Mathematics 2019-09-04 Xing-Bin Pan , Zhibing Zhang

In this work, we study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending two recent results, we provide a recipe that allows one to relate resonant transmission spectra…

General Relativity and Quantum Cosmology · Physics 2024-10-01 Saulo Albuquerque , Sebastian H. Völkel , Kostas D. Kokkotas , Valdir B. Bezerra

In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…

General Relativity and Quantum Cosmology · Physics 2010-09-06 Oscar Reula , Olivier Sarbach

We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body by means of the so called local Neumann to Dirichlet map on a curved portion $\Sigma$ of the boundary. Motivated by the uniqueness result for…

Analysis of PDEs · Mathematics 2023-03-31 Giovanni Alessandrini , Romina Gaburro , Eva Sincich

The inverse problem of determining the cross-sectional area of a human vocal tract during the utterance of a vowel is considered. The frequency-dependent boundary condition at the lips is expressed in terms of the acoustic impedance of a…

Mathematical Physics · Physics 2021-03-16 Tuncay Aktosun , Paul Sacks , Xiao-Chuan Xu

The focus of this paper is the study of the regularity properties of the time harmonic Maxwell's equations with anisotropic complex coefficients, in a bounded domain with $C^{1,1}$ boundary. We assume that at least one of the material…

Analysis of PDEs · Mathematics 2015-02-19 Giovanni S. Alberti , Yves Capdeboscq

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schr\"odinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics…

Analysis of PDEs · Mathematics 2015-05-04 Ru-Yu Lai , Victor Isakov , Jenn-Nan Wang

This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based…

Analysis of PDEs · Mathematics 2011-05-23 Dirk Pauly , Sergey Repin

Inverse problems, which are related to Maxwell's equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such…

Numerical Analysis · Mathematics 2024-10-08 Vincenzo Mottola , Antonio Corbo Esposito , Gianpaolo Piscitelli , Antonello Tamburrino

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…

Analysis of PDEs · Mathematics 2026-04-17 Gunther Uhlmann , Yuchao Yi , Jian Zhai

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

Analysis of PDEs · Mathematics 2022-07-15 Jaan Janno , Yavar Kian

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

Analysis of PDEs · Mathematics 2024-09-11 L Baudouin , A Imba , A Mercado , A Osses