title: On Maxwell's equations in non-stationary media.
abstract: Maxwell's equations formulated for media with gradually changing conductivity are reduced to Volterra integral equations. Analytical and numerical investigations of the equations are presented for the case of gradual splash-like change in conductivity. Splash-like change in medium parameters can model any discharge phenomena, growing plasma, charge injection, etc. Exact analytical solution for the resolvent is presented and different field behaviours are analysed for the incident field as a plane wave and as an impulse.
authors.affiliation: School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, UK. iv4@st-andrews.ac.uk
authors.forename: I
authors.initials: I
authors.lastname: Vorgul