We consider self-propelled particles confined between two parallel plates, moving with a constant velocity while their moving direction changes by rotational diffusion. The probability distribution of such micro-organisms in confined environment is singular because particles accumulate at the boundaries. This leads us to distinguish between the probability distribution densities in the bulk and in the boundaries. They satisfy a degenerate Fokker–Planck system and we propose boundary conditions that take into account the switching between free-moving and boundary-contacting particles. Relative entropy property, a priori estimates and the convergence to an unique steady state are established. The steady states of both the PDE and individual based stochastic models are compared numerically.

我们考虑限制在两个平行板之间的自推进粒子，它们以恒定速度移动，而它们的移动方向通过旋转扩散而改变。这种微生物在密闭环境中的概率分布是奇异的，因为粒子在边界处积聚。这使我们能够区分体中和边界中的概率分布密度。它们满足退化的 Fokker-Planck 系统，我们提出了考虑自由移动和边界接触粒子之间切换的边界条件。建立相对熵属性、先验估计和收敛到唯一稳定状态。对 PDE 和基于个体的随机模型的稳态进行了数值比较。