The problem of determining the kernel of electrodynamics equations for dispersion media
type: Item
instance of: scholarly article
title: The problem of determining the kernel of electrodynamics equations for dispersion media
zbMATH Open document ID: 1237.78004
DOI: 10.1134/S1064562411060068
published in: Doklady Mathematics
publication date: 2012-01-06T00:00:00Z
review text: The propagation of electromagnetic waves in dispersion media is described by equations for \(E(x,t)\) and \(H(x,t)\) with the convolution term \(\varepsilon_0(x)p(x) \int_{-\infty}^t k(t-s) E(x,s)\,ds\), where \(\varepsilon_0(x)\) stands for the dielectric permeability. The external current has the form of a delta-function \(j_0 \delta(x-y,t)\) concentrated at \(y \in \mathbb R^3\). The author considers the following inverse problem. Given a domain \(\Omega \subset \mathbb R^3\), assume that \(H(x,y,t)\) is known for all \(x,y \in \partial \Omega\) and all \(t < \tau(x,y)+\eta\). It is required to determine \(\varepsilon_0(x)\) and \(p(x)\) on \(\Omega\).
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 5995550
zbMATH Keywords: electromagnetic wave
zbMATH Keywords: medium dispersion
zbMATH Keywords: inverse problem for coefficient
author: Vladimir G. Romanov
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
cites work: Q3697429
description: scientific article; zbMATH DE number 5995550