Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations

Abstract

We investigate the evolution of the probability distribution function in time for some wave and Maxwell equations in random media for which the parameters, e.g. permeability, permittivity, fluctuate randomly in space; more precisely, two different media interface randomly in space. We numerically compute the probability distribution and density for output solutions. The underlying numerical and statistical techniques are the so-called polynomial chaos Galerkin projection, which has been extensively used for simulating partial differential equations with uncertainties, and the Monte Carlo simulations.