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

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20 Hadeler , K. P. , Kuttler , C. ( 1999 ). Dynamical models for granular matter . Granular Matter 2 : 9 – 18 . [Google Scholar]], 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.