On the applicability of the perturbation method for the random viscous Burgers’ equation

Abstract

A classical problem in uncertainty quantification is the analysis of the steady-state solution to the viscous Burgers’ equation subject to a small random perturbation at the boundary. The perturbation method, introduced in the sixties by Crandall to study nonlinear vibrations, expands the stochastic solution as a mean square power series in terms of the centered perturbation. We show that the perturbation method does work to quantify the uncertainty for the location of the transition layer of the steady-state solution.