# Preprint 2008-023

# Global Existence of Large BV Solutions in a Model of Granular Flow

## Debora Amadori and Wen Shen

**Abstract:**
In this paper we analyze a set of equations proposed by Hadeler and
Kuttler, describing the flow of granular matter in terms
of the heights of a standing layer and of a moving layer. By a
suitable change of variables, the system can be written as a
2×2 hyperbolic system of balance laws, which we study in the
one-dimensional case. The system is linearly degenerate along two
straight lines in the phase plane, and therefore is weakly linearly
degenerate at the point of the intersection. The source term is
quadratic, consisting of product of two quantities, which are
transported with strictly different speeds. Assuming that the
initial height of the moving layer is sufficiently small, we prove
the global existence of entropy-weak solutions to the Cauchy
problem, for a class of initial data with bounded but possibly large
total variation.