Random systems of conservation laws

We aim to investigate a particular 2x2 system of conservation laws which contains randomness, either in the parameters in the equation, or in the initial data. Concretely we plan to establish a proper notion of random solutions, prove the existence of su ch solutions, and find numerical methods for calculating approximations to these solutions. Furthermore, these numerical methods shall also be used to estimate statistical parameters such as the mean, variance and kurtosis of the ensemble of solutions. We hope to accomplish this through a series of visits from Oslo to Würzburg and vice versa.