Boundary conditions and existence results for levermore's moments system

This paper considers the 14 moment expansion of the Boltzmann equation proposed by D. Levermore. After a brief review of this model, we derive weak boundary conditions compatible with the hyperbolic structure of the model, and express in average the microscopic boundary conditions imposed to the gas. This choice of half flux boundary conditions is justified by a mathematical analysis of the resulting linearized problem. Using standard parabolic regularization arguments and a specific dissipation inequality, we prove that the linearized problem has a unique solution.