L1 stability estimate for a one-dimensional Boltzmann equation with inelastic collisions

In this paper, we study the L1 stability of a one-dimensional Boltzmann equation on the line with inelastic collisions in Rend. Sem. Mat. Fis. Milano 67 (1997) 169–179. Under the suitable assumptions on the initial data, we construct a nonlinear functional which measures L1 distance between two mild solutions, and is nonincreasing in time t. Using the time-decay estimate of , we show that mild solutions are L1-stable: where G is a positive constant independent of time t, f and are mild solutions corresponding to initial data f0 and in L1(R2)∩L+∞(R2), respectively.