On the Blow-up for a Discrete Boltzmann Equation in the Plane
  We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed. 
Alberto Bressan and Massimo Fonte