We consider a 2×2 system of hyperbolic balance laws, in one-space dimension, that describes the evolution of a granular material with slow erosion and deposition. The dynamics is expressed in terms of the thickness of a moving layer on top and of a standing layer at the bottom. The system is linearly degenerate along two straight lines in the phase plane and genuinely nonlinear in the subdomains confined by such lines. In particular, the characteristic speed of the first characteristic family is strictly increasing in the region above the line of linear degeneracy and strictly decreasing in the region below such a line. The non dissipative source term is the product of two quantities that are transported with the two different characteristic speeds.
The global existence of entropy weak solutions of the Cauchy problem for such a system was established by Amadori and Shen for initial data with bounded but possibly large total variation, under the assumption that the initial height of the moving layer be sufficiently small.
