On measure-valued solutions to a two-dimensional gravity-driven avalanche flow model

This paper concerns measure-valued solutions for the two-dimensional granular avalanche flow model introduced by Savage and Hutter. The system is similar to the isentropic compressible Euler equations, except for a Coulomb–Mohr friction law in the source term. We will partially follow the study of measure-valued solutions given by DiPerna and Majda. However, due to the multi-valued nature of the friction law, new more sensitive measures must be introduced. The main idea is to consider the class of x-dependent maximal monotone graphs of non-single-valued operators and their relation with 1-Lipschitz, Carathéodory functions. This relation allows to introduce generalized Young measures for x-dependent maximal monotone graph.