标题： 离散速度动能方程的长时间行为 显示英文标题

标题： Long time behavior of discrete velocity kinetic equations

摘要： 我们研究在周期性边界条件下，一维和三维非线性离散速度动力学方程的长时间行为。 我们证明了解在$L^2$空间中指数时间衰减到全局平衡。 我们的结果适用于包括 Goldstein-Taylor 和 Carleman 方程在内的广泛相互作用率类，收敛速率的估计是显式且可构造的。 该技术基于通过修改 Boltzmann 熵来构建合适的 Lyapunov 泛函。 显示英文摘要

摘要： We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the $L^2$ space. Our result holds for a wide class of interaction rates including the Goldstein-Taylor and Carleman equations, and the estimates on the rate of convergence are explicit and constructive. The technique is based on the construction of suitable Lyapunov functionals by modifying Boltzmann's entropy.