PDF's Of The Burgers Equation On The Semiline With Fluctuating Flux At The Origin
arXiv:cond-mat/9808002 · doi:10.1016/S0375-9601(99)00285-6
Abstract
We derive the asymptotic behaviour of the one point probability density for the inhomogeneous shock slopes in the turbulent regime, when a Gaussian fluctuating flux at origin derives the system. We also calculate the time dependence of the beyond which there won't exists any velocity shocks as $ x_{f}\cong t^{3/4}{(log{t})}^{1\4}$. We argue that the stationary state of the problem would be equivalent with the long time limit of the diffusion equation with arandom source at origin.
10 paged Text, 2 Postscript figures