We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper boundary conditions should be prescribed. Utilizing an orthogonal decomposition, we separate the part with a damping term from the system and then impose a new class of Maxwell-type boundary conditions on it. Due to the new boundary condition, we show that the half-space boundary value problem admits a unique solution with explicit expressions. Instantly, the well-posedness of the linear moment system is achieved. We apply the procedure to classical flow problems with the Shakhov collision term, such as the velocity slip and temperature jump problems. The model can capture Knudsen layers with very high accuracy using only a few moments.

翻译：我们为半空的线性时空系统建议一个条件精密的 Maxwell 类型的边界条件。 作为 Boltzmann 方程式的缩减, 此时方程式可用于在固态墙附近模拟 Knudsen 层, 应该在此指定适当的边界条件 。 使用正方形分解, 我们将这部分与系统分开, 然后对它施加一个新的等级的 Maxwell 型的边界条件 。 由于新的边界条件, 我们显示半空边界值问题以明确的表达方式承认了一个独特的解决方案 。 即时, 线性时时间系统已经实现 。 我们应用程序来处理沙克夫碰撞术语的典型流程问题, 比如速度滑和温度跳跃问题 。 模型可以使用短短的片段来非常精确地捕捉 Knudsen 层 。