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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

We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand…

Analysis of PDEs · Mathematics 2011-05-23 Dirk Pauly

In this paper, a novel time domain sampling method based on the initial arrival time of waves is proposed to reconstruct acoustic sources, including point sources, curve sources, surface sources and block sources. The uniqueness of…

Mathematical Physics · Physics 2025-09-30 Qiuyi Li , Bo Chen , Peng Gao , Yu Sun , Yao Sun

Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…

Numerical Analysis · Mathematics 2025-06-02 Yakov Berchenko-Kogan , Ari Stern

We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…

Systems and Control · Computer Science 2017-01-04 Christopher A. Beattie , Serkan Gugercin , Volker Mehrmann

In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

Analysis of PDEs · Mathematics 2021-04-27 Ibtissem Ben Aïcha , Guanghui Hu , Manmohan Vashisth , Jun Zou

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

The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell's equations, a reduced system of equations governing the dynamics of the electric and polarization fields are obtained.…

Exactly Solvable and Integrable Systems · Physics 2025-10-14 Mark J. Ablowitz , Ramesh Gupta , Ziad H. Musslimani , Nicholas J. Ossi

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…

Computational Physics · Physics 2023-07-25 Damian P. San Roman Alerigi , David I. Ketcheson , Boon S. Ooi

In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…

Analysis of PDEs · Mathematics 2026-04-07 Rahul Bhardwaj , Mandeep Kumar , Manmohan Vashisth

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

This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…

Analysis of PDEs · Mathematics 2025-09-17 Jone Apraiz , Anna Doubova , Enrique Fernández-Cara , Masahiro Yamamoto

Magnetic reconnection in an antiparallel uniform Harris current sheet equilibrium, which is initially perturbed by a region of enhanced resistivity limited in all three dimensions, is investigated through compressible magnetohydrodynamic…

Astrophysics · Physics 2009-10-31 Joerg Schumacher , Bernhard Kliem , Norbert Seehafer

By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…

Mathematical Physics · Physics 2019-11-14 Florio M. Ciaglia , Fabio Di Cosmo , Giuseppe Marmo , Luca Schiavone

In this work, we propose a full-waveform technique for the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion. The approach is formulated in the frequency domain, and…

Computational Physics · Physics 2020-07-15 Alan A. S. Amad , Antonio A. Novotny , Bojan B. Guzina

This article aims to present a general analysis of a class of inverse problems that consists in recovering the elliptic parameter maps in systems of PDEs, such as the linear elastic system, from the knowledge of some of their solutions.…

Analysis of PDEs · Mathematics 2025-05-26 Élie Bretin , Eliott Kacedan , Laurent Seppecher

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…

Analysis of PDEs · Mathematics 2009-02-25 Pedro Caro , Petri Ola , Mikko Salo

This paper presents a practical case study of a data-driven magnetostatic finite element solver applied to a real-world three-dimensional problem. Instead of using a hard-coded phenomenological material model within the solver, the…

Computational Engineering, Finance, and Science · Computer Science 2021-12-03 Armin Galetzka , Dimitrios Loukrezis , Herbert De Gersem

The Darwin field model addresses an approximation to Maxwell's equations where radiation effects are neglected. It allows to describe general quasistatic electromagnetic field phenomena including inductive, resistive and capacitive effects.…

Computational Engineering, Finance, and Science · Computer Science 2020-03-13 Markus Clemens , Bernhard Kähne , Sebastian Schöps

Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…

General Relativity and Quantum Cosmology · Physics 2016-03-01 Li-Xin Li