The problem of determining the kernel of electrodynamics equations for dispersion media
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 \(\Omega\).
scientific article; zbMATH DE number 5995550