论文标题
与随机系数线性化BGK方程的低调
Hypocoercivity of the linearized BGK-equation with stochastic coefficients
论文作者
论文摘要
在本文中，我们研究了随机性对一个维度线性化BGK模型的影响。我们证明了对全球平衡的指数衰减率。该衰减率可以被证明独立于物理合理规范中的随机影响。我们将进一步讨论有关解决方案随机变量的$ n $ Th衍生物的衰减率。我们的策略基于Lyapunov的方法。我们需要进行Lyapunov估计的矩阵现在取决于随机变量。这需要仔细分析随机效应。
In this paper we study the effect of randomness on a linearized BGK-model in one dimension. We prove exponential decay rate to a global equilibrium. This decay rate can be proven to be independent of the stochastic influence in a physical reasonable norm. We will further discuss the decay rate of the $n$-th derivative with respect to the stochastic variable of the solutions. Our strategy is based on Lyapunov's method. The matrices we need for a Lyapunov's estimate now depend on the stochastic variable. This requires a careful analysis of the random effect.
