论文标题
用于化学反应气体的固定BGK模型
Stationary BGK models for chemically reacting gas in a slab
论文作者
论文摘要
我们研究了两个固定BGK型模型的边界值问题 - 快速化学反应的BGK模型和用于缓慢化学反应的BGK模型 - 并提供了一个统一的论点，以确定平板中反应性BGK模型的固定流量的存在和独特性。对于这两种模型，主要难度是在从上和下方对反应性参数的均匀控制中出现的，因为与非反应性气体的BGK模型不同，反应性BGK模型的反应性参数是通过高度非线性关系来定义的。为了克服这一难度，我们引入了几种非线性功能，这些功能捕获了这种非线性关系的基本结构，例如特定变量中的单调性，使人们能够得出反应性平衡系数的必要估计。
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 arises in the uniform control of the reactive parameters from above and below, since, unlike the BGK models for non-reactive gases, the reactive 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 reactive equilibrium coefficients.
