We consider scalar hyperbolic conservation laws in several space dimensions, with a class of random (and parametric) flux functions. We propose a Karhunen–Loève expansion on the state space of the random flux. For random flux functions which are Lipschitz continuous with respect to the state variable, we prove the existence of a unique random entropy solution. Using a Karhunen–Loève spectral decomposition of the random flux into principal ...

We consider stochastic multi-dimensional linear hyperbolic systems of conservation laws. We prove existence and uniqueness of a random weak solution, provide estimates for the regularity of the solution in terms of regularities of input data, and show existence of statistical moments. Bounds for mean square error vs. expected work are proved for the Multi-Level Monte Carlo Finite Volume algorithm which is used to approximate the moments ...