Statistical moments for solutions of non-linear scalar equations with random Riemann data

In this paper we generalize the solution of random Riemann problem for a scalar equation, for flux function with one inflection point. We introduce both a bifurcation theory for the state space (uL, uR) and an efficient numerical method. The statistical moments are obtained from a computable integral exact form. We present some numerical results, considering an uniform distribution, and a bivariate normal distribution. We obtain very good results compared with the solution obtained with Monte Carlo.