  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.
