Hypocoercivity methods are applied to linear kinetic equations without any space confinement, when local equilibria have a sub-exponential decay. By Nash type estimates, global rates of decay are obtained, which reflect the behavior of the heat equation obtained in the diffusion limit. The method applies to Fokker-Planck and scattering collision operators. The main tools are a weighted Poincare inequality (in the Fokker-Planck case) and norms with various weights. The advantage of weighted Poincare inequalities compared to the more classical weak Poincare inequalities is that the description of the convergence rates to the local equilibrium does not require extra regularity assumptions to cover the transition from super-exponential and exponential local equilibria to sub-exponential local equilibria.

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矫顽力和次指数局部均衡

当局部平衡具有次指数衰减时，低矫顽力方法应用于没有任何空间限制的线性动力学方程。通过 Nash 类型估计，获得了全局衰减率，这反映了在扩散极限中获得的热方程的行为。该方法适用于 Fokker-Planck 和散射碰撞算子。主要工具是加权 Poincare 不等式（在 Fokker-Planck 案例中）和具有不同权重的规范。与更经典的弱 Poincare 不等式相比，加权 Poincare 不等式的优势在于，对局部均衡收敛速度的描述不需要额外的正则假设来涵盖从超指数和指数局部均衡到次指数局部均衡的转变.