L1 stability for the one-dimensional broadwell model of a discrete velocity gas

We prove L-1 stability for the one-dimensional Broadwell model for a discrete velocity gas. For initial data in L-1 (R) boolean AND L-+(infinity) (R) with small mass, we show that bounded mild solutions are L-1-stable. For this, we employ a nonlinear functional H(t) that is equivalent to the L-1 distance between two mild solutions and non-increasing in time t.