A boundary value problem for the stationary Boltzmann equation with hard sphere in a half-space is considered for a binary mixture of gases, imposing slightly perturbed reflection boundary conditions for the both species. We assume that one of the species is dominant and close to equilibrium but the density of the other is small. Under this assumption, we prove the existence and uniqueness of the solution to the coupled system, and their accurate asymptotic behavior in the far field is obtained. Our result is based on the one species result. However, the system is not symmetric which leads us to the major difficulty in this paper. Thanks to the conservation laws for the collision operators, the nonlinear problem is solved.

对于气体的二元混合物，考虑半空间中具有硬球的静止玻尔兹曼方程的边界值问题，对两种物质施加轻微扰动的反射边界条件。我们假设其中一个物种占优势并接近平衡，但另一个物种的密度很小。在这个假设下，我们证明了耦合系统解的存在性和唯一性，得到了它们在远场的精确渐近行为。我们的结果是基于一个物种的结果。 然而，该系统是不对称的，这导致了我们在本文中遇到的主要困难。由于碰撞算子的守恒定律，非线性问题得以解决。