半空间动能方程与一般边界条件
Half-space Kinetic Equations with General Boundary Conditions
AI总结：
研究半空间线性动能方程的一般边界条件，包括给定的入射数据和多种反射类型，扩展了之前的工作。采用阻尼添加-移除技术，证明了线性方程的适定性及数值方案的拟最优性，并通过实例验证。
摘要：
我们研究了包含给定入射数据和多种反射类型的半空间线性动能方程的一般边界条件，扩展了之前的工作[LLS14]。与[LLS14]类似，主要技术是阻尼添加-移除过程。我们建立了具有一般边界条件的线性（或线性化）半空间方程的适定性，并证明了数值方案的拟最优性。数值方法通过包括双物种传输方程、多频传输方程以及二维速度空间中的线性化BGK方程的实例进行了验证。
英文摘要：
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.
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