论文标题
多原子单加气模型的线性化Boltzmann操作员的Fredholm特性
Fredholm Property of the Linearized Boltzmann Operator for a Polyatomic Single Gas Model
论文作者
论文摘要
在以下工作中，我们考虑通过连续变量代表微观内部能量来对多原子气体进行建模的Boltzmann方程。在碰撞横截面$ \ MATHCAL {B} $的一些便利假设下，我们证明了线性化的Boltzmann boltzmann operator $ \ nathcal $ \ nathcal {l} $ of this Modal of this Modal is Modal is a frholm是fr的。为此，我们将$ \ MATHCAL {L} $写为碰撞频率运算符的扰动，并证明扰动运算符$ \ Mathcal {K k} $是紧凑的。在检查$ \ Mathcal {k} $的内核形式后建立了结果，并使用基本参数证明其在其域上可以在其域上进行$ l^2 $。
In the following work, we consider the Boltzmann equation that models a polyatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section $\mathcal{B}$, we prove that the linearized Boltzmann operator $\mathcal{L}$ of this model is a Fredholm operator. For this, we write $\mathcal{L}$ as a perturbation of the collision frequency multiplication operator, and we prove that the perturbation operator $\mathcal{K}$ is compact. The result is established after inspecting the kernel form of $\mathcal{K}$ and proving it to be $L^2$ integrable over its domain using elementary arguments.
