WHITE-NOISE PERTURBATION OF THE VISCOUS SHOCK FRONTS OF THE BURGERS-EQUATION

We study the front dynamics of solutions of the initial value problem of the Burgers equation with initial data being the viscous shock fron t plus the white noise perturbation. In the sense of distribution, the solutions propagate with the same speed as the unperturbed front, how ever, the front location is random and satisfies a central limit theor em with the variance proportional to the time t, as t goes to infinity . With probability arbitrarily close to one, the front width is O(1) f or large time.