Boundary Layer Solution of the Boltzmann Equation for Diffusive Reflection Boundary Conditions in Half-Space

We study steady Boltzmann equation in half-space, which arises the Knudsen boundary layer problem, with diffusive reflection conditions. Under certain admissible conditions and source term decaying exponentially, we establish existence of solution for both linear nonlinear half-space condition $L^\infty_{x,v}$ when far-field Mach number Maxwellian is zero. The continuity spacial decay are obtained. uniqueness established under some constraint