Maxwell's Equations with Scalar Impedance: Inverse Problems with data given on a part of the boundary
| dc.creator | Kurylev, Yaroslav | |
| dc.creator | Lassas, Matti | |
| dc.creator | Somersalo, Erkki | |
| dc.date | 2005-04-15 | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:19:09Z | |
| dc.date.available | 2026-07-07T05:19:09Z | |
| dc.description | We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $α$. This means that the material is conformal, i.e., the electric permittivity $ε$ and magnetic permeability $μ$ are tensors satisfying $μ=α^2ε$. This condition is equivalent to a single propagation speed of waves with different polarizations which uniquely defines an underlying Riemannian structure. The analysis is based on an invariant formulation of the system of electrodynamics as a Dirac type first order system on a Riemannian $3-$manifold with an additional structure of the wave impedance, $(M,g,α)$, where $g$ is the travel-time metric. We study the properties of this system in the first part of the paper. In the second part we consider the inverse problem, that is, the determination of $(M,g,α)$ from measurements done only on an open part of the boundary and on a finite time interval. As an application, in the isotropic case with $M\subset \R^3$, we prove that the boundary data given only on an open part of the boundary determine uniquely the domain $M$ and the coefficients $ε$ and $μ$. | |
| dc.identifier | https://arxiv.org/abs/math/0504320 | |
| dc.identifier | http://arxiv.org/abs/math/0504320 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74913 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J45, 35R30, 35Q60 | |
| dc.title | Maxwell's Equations with Scalar Impedance: Inverse Problems with data given on a part of the boundary | |
| dc.type | text |