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We propose a necessary and sufficient condition for the well-posedness of thelinear non-homogeneous Grad moment equations in half-space. The Grad momentsystem is based on Hermite expansion and regarded as an efficient reductionmodel of the Boltzmann equation. At a solid wall, the moment equations arecommonly equipped with a Maxwell-type boundary condition named the Gradboundary condition. We point out that the Grad boundary condition is unstablefor the non-homogeneous half-space problem. Thanks to the proposed criteria, weverify the well-posedness of a class of modified boundary conditions. Thetechnique to make sure the existence and uniqueness mainly includes awell-designed preliminary simultaneous transformation of the coefficientmatrices and Kreiss' procedure about the linear boundary value problem withcharacteristic boundaries. The stability is established by a weighted estimate.At the same time, we obtain the analytical expressions of the solution, whichmay help solve the half-space problem efficiently.

On Well-posed Boundary Conditions for the Linear Non-homogeneous Moment Equations in Half-space