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Related papers: On global uniqueness for an IBVP for the time-harm…

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A first-order ordinary differential equation, solved with respect to derivative, is considered. It's right-hand side is defined and continuous on the set, consisting of a connected open subset of a two-dimensional Euclidean space and a part…

Classical Analysis and ODEs · Mathematics 2024-02-27 Vladimir V. Basov

We embed general boundary value problems for the time-harmonic Maxwell equations into the elliptic boundary value theory. This is achieved by introducing two new scalar functions to the electromagnetic field and imposing additional boundary…

Analysis of PDEs · Mathematics 2026-04-06 Yuri A. Godin , Boris Vainberg

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…

Spectral Theory · Mathematics 2012-12-07 Lung-Hui Chen

We consider for the full time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic boundary measurements…

Analysis of PDEs · Mathematics 2009-12-08 C. Daveau , A. Khelifi

In this third work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted DIrichlet boundary conditions on a finite timelike boundary. The boundary conditions…

General Relativity and Quantum Cosmology · Physics 2025-12-30 Zhongshan An , Michael T. Anderson

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 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

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…

General Relativity and Quantum Cosmology · Physics 2018-12-27 István Rácz

We consider the problem of recovering of initial data in the IBVP for the wave-type equation in the half-space by the solution restricted to the boundary. The singular value decomposition of this problem is concerned: the asymptotics of…

Spectral Theory · Mathematics 2015-06-19 M. N. Demchenko

We consider the dynamical inverse problem for the Maxwell system on a Riemannian 3-manifold with boundary in a time-optimal set-up. Using BC-method we show that the data of the inverse problem (electromagnetic measurements on the boundary)…

Mathematical Physics · Physics 2012-06-01 M. I. Belishev , M. N. Demchenko

We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…

Analysis of PDEs · Mathematics 2025-10-17 Ben Schweizer , David Wiedemann

In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…

Analysis of PDEs · Mathematics 2018-05-30 Martin Spitz

In this paper, we extend and simplify the methods in [13] to improve the results on uniqueness of the boundary determination for the Maxwell equation. In particular, we show that the electromagnetic parameters are uniquely determined to…

Analysis of PDEs · Mathematics 2025-10-30 Chengyu Wu , Jiaqing Yang

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

In this paper well-posedness is proved for an initial and boundary value problem (IBVP) relative to a large class of quasilinear hyperbolic systems, in $p+q$ equations, on a strip, arising from a model of $H_2O$-phase transitions in the…

Analysis of PDEs · Mathematics 2014-11-11 Steave C. Selvaduray

In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…

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

We consider the initial boundary value problem (IBVP) for a non-local scalar conservation laws in one space dimension. The non-local operator in the flux function is not a mere convolution product, but it is assumed to be aware of…

Analysis of PDEs · Mathematics 2018-11-26 Paola Goatin , Elena Rossi

In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term $\epsilon\partial_t u-\nabla\cdot(\gamma\nabla u^m)+\lambda u^q=0$, with…

Analysis of PDEs · Mathematics 2021-12-16 Cătălin I. Cârstea , Tuhin Ghosh , Gunther Uhlmann

In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured…

Analysis of PDEs · Mathematics 2015-02-06 Francis J. Chung , Petri Ola , Mikko Salo , Leo Tzou