Esaim: Control, Optimisation and Calculus of Variations Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
Esaim: Control, Optimisation and Calculus of Variations Homogenization and Diffusion Asymptotics of the Linear Boltzmann Equation
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Esaim：线性玻尔兹曼方程的变分均匀化和扩散渐近的控制、优化和微积分
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通讯作者：
A. Mellet
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作者：
T. Goudon;A. Mellet
我们研究了具有振荡系数的一般守恒Boltzmann方程的扩散极限。振荡的频率与平均自由程的倒数具有相同的阶次，并且系数可能取决于慢变量和快变量。超过极限，我们得到了一个有效的漂移扩散方程。我们还描述了当平衡函数具有非零通量时的扩散行为。
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.