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

Oslenne Araújo; Patrícia Gonçalves; Alexandre B. Simas

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arXiv · 2304.03634

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

Oslenne Araújo·Patrícia Gonçalves·Alexandre B. Simas

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Abstract

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 $\theta$.

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Oslenne Araújo, Patrícia Gonçalves, Alexandre B. Simas. 2023-04-07. Hydrodynamic limit of the multi-component slow boundary WASEP with collisions. https://arxiv.org/abs/2304.03634

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