  In this paper, we study the initial value problem of a Boltzmann type
equation with a nonlinear degenerate damping. We prove the existence of global
weak solutions with large initial data, in three dimensional space. We rely on
a variant version of the Gronwall inequality and $L^p$ regularity of average
velocities to derive the compactness of solutions to a suitable approximation.
This allows us to recover a weak solution by passing to the limits. After the
existence result, we also prove energy conservation for the weak solution under
some certain condition.
