Robust Design of Initial Boundary Value Problems

We study hyperbolic and incompletely parabolic systems with stochastic boundary and initial data. Estimates of the variance of the solution are presented both analytically and numerically. It is shown that one can reduce the variance for a given input, with a specific choice of boundary condition. The technique is applied to the Maxwell, Euler, and Navier–Stokes equations. Numerical calculations corroborate the theoretical conclusions.