论文标题
在代数为平均值的情况下，线性玻尔兹曼方程的均质化
Homogenization of Linear Boltzmann Equations in the Context of Algebras with Mean Value
论文作者
论文摘要
该论文涉及通过Sigma-Convergence方法的均值对线性玻尔兹曼方程的均质化。在对方程系数的一般确定性假设下，我们证明颗粒的密度会收敛到漂移扩散方程的溶液。为了实现我们的目标，我们将Krein-Rutman定理与Fredholm替代方案一起用于局部凸出空间，以解决所谓的校正问题。
The paper deals with the homogenization of a linear Boltzmann equation by the means of the sigma-convergence method. Under a general deterministic assumption on the coefficients of the equation, we prove that the density of the particles converges to a solution of a drift-diffusion equation. To achieve our goal, we use the Krein-Rutman theorem for locally convex spaces together with the Fredholm alternative to solve the so-called corrector problem.
