Stationary BGK Models for Chemically Reacting Gas in a Slab

We study the boundary value problem of two stationary BGK-type models—the BGK model for fast chemical reaction and the BGK model for slow chemical reaction—and provide a unified argument to establish the existence and uniqueness of stationary flows of reactive BGK models in a slab. For both models, the main difficulty arise in the uniform control of the auxiliary parameters from above and below, since, unlike the BGK models for non-reactive gases, the auxiliary parameters for the reactive BGK models are defined through highly nonlinear relations. To overcome this difficulty, we introduce several nonlinear functionals that capture essential structures of such nonlinear relations such as the monotonicity in specific variables, that enable one to derive necessary estimates for the auxiliary parameters.