We consider random scalar hyperbolic conservation laws (RSCLs) in spatial dimension $d\ge 1$ with bounded random flux functions which are $\mathbb{P}$-a.s. Lipschitz continuous with respect to the state variable, for which there exists a unique random entropy solution (i.e., a measurable mapping from the probability space into $C(0,T;L^1(\mathbb{R}^d))$ with finite second moments). We present a convergence analysis of a Multi-Level ...

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 ...