  We prove quantitative growth estimates for large data solutions to the 1D
Boltzmann equation, for a collision kernel with angular cutoff and relative
velocity cutoff. We present proofs for the global well-posedness results
presented in the note of Biryuk, Craig, and Panferov, in which global solutions
for this equation are shown to exist for large data, with density bounded for
all time. We show that these solutions propagate moments in $v$, and
derivatives in $x$ and $v$. Our main contribution is to develop new, sharp
integral inequality estimates, which allow us to prove exponential growth
bounds in $L^\infty_x L^1_v$ for large data, and to prove dissipation in $
L^\infty_x L^1_v$ for finite energy data on the line.
