Abstract
The reducibility to differential forms of certain nonlinear integral operators appearing in kinetic theory is discussed in the frame of a stationary problem in gas dynamics with removal events. A wide class of transition kernels allowing such reducibility is characterized, and the validity of these kernels as approximations to real ones is studied in terms of their asymptotic behaviour for large and small velocities. In fact, this behaviour is shown to determine the corresponding limiting velocity dependence in the solutions to the kinetic equation.