We analyze the regularity of random entropy solutions to scalar hyperbolic conservation laws with random initial data. We prove regularity theorems for statistics of random entropy solutions like expectation, variance, space-time correlation functions and polynomial moments such as gPC coefficients. We show how regularity of such moments (statistical and polynomial chaos) of random entropy solutions depends on the regularity of the distribution law of the random shock location of the initial data....

In this work we describe an efficient model for the simulation of a two-phase flow made of a gas and a granular solid. The starting point is the two-velocity two-pressure model of Baer and Nunziato [Int. J. Multiph. Flow16 (1986) 861–889]. The model is supplemented by a relaxation source term in order to take into account the pressure equilibrium between the two phases and the granular stress in the solid phase. We show that the relaxation process can be made thermodynamically coherent with an...