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We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.

Analysis of PDEs · Mathematics 2020-01-24 Rohit Kumar Mishra , Manmohan Vashisth

This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…

Analysis of PDEs · Mathematics 2018-04-26 Cătălin I. Cârstea

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

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

We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We show that a…

Analysis of PDEs · Mathematics 2012-12-07 John M. Ball , Yves Capdeboscq , Basang Tsering Xiao

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

We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…

Analysis of PDEs · Mathematics 2020-07-20 Frank Osterbrink , Dirk Pauly

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…

Analysis of PDEs · Mathematics 2020-10-19 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Mahran Rihani

This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…

Numerical Analysis · Mathematics 2020-07-06 Larisa Beilina , Vitoriano Ruas

We consider solutions to the time-harmonic Maxwell problem in $\R^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of…

Mathematical Physics · Physics 2007-06-01 Christian Daveau , Abdessatar Khelifi

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…

General Relativity and Quantum Cosmology · Physics 2008-11-22 Oliver Rinne

We consider an inverse boundary value problem for Maxwell's equations, which aims to recover the electromagnetic material properties of a body from measurements on the boundary. We show that a Lipschitz continuous conductivity, electric…

Analysis of PDEs · Mathematics 2018-07-11 Monika Pichler

In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…

Analysis of PDEs · Mathematics 2016-10-06 Antonino Morassi , Edi Rosset

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

The article deals with electrodynamics in the presence of anisotropic materials having scalar wave impedance. Maxwell's equations written for differential forms over a 3-manifold are analysed. The system is extended to a Dirac type first…

Analysis of PDEs · Mathematics 2007-05-23 Yaroslav Kurylev , Matti Lassas , Erkki Somersalo

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…

Analysis of PDEs · Mathematics 2021-11-24 Yavar Kian , Yosra Soussi

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

We consider a parabolic equation in a bounded domain $\OOO$ over a time interval $(0,T)$ with the homogeneous Neumann boundary condition. We arbitrarily choose a subboundary $\Gamma \subset \ppp\OOO$. Then, we discuss an inverse problem of…

Analysis of PDEs · Mathematics 2022-11-23 O. Imanuvilov , M. Yamamoto

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 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