Hydrodynamic limit of the multi-component slow boundary WASEP with collisions

In this article, we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists in a superposition of several dynamics: the exclusion rule, that dictates that no more than a particle per site with a fixed velocity is allowed; a collision dynamics, that dictates that particles at the same site can collide and originate particles with new velocities such that the linear momentum is conserved; a boundary dynamics that injects and removes particle in the system. This last dynamics destroys the conservation law, and its strength is regulated by a parameter $\theta$. The goal is the derivation of the hydrodynamic limit, and the boundary conditions change drastically according to the value of $\theta$.