一类动力学模型的亚强制松弛到平衡态的三阶微分不等式
Hypocoercive relaxation to equilibrium for some kinetic models via a third order differential inequality
摘要：
本文研究了一些特殊的动力学模型，其中随机性仅作用于速度变量水平。通常，马尔可夫生成元不能满足任何庞加莱不等式。因此，没有Gronwall引理可以容易地导致Ft的指数衰减（沿着半群的检验函数的L2范数）。然而，对于动力学Fokker-Planck动力学和分段确定性演化，我们证明了Ft满足一个三阶微分不等式，它给出了一个明确的收敛速率。
英文摘要：
This paper deals with the study of some particular kinetic models, where the randomness acts only on the velocity variable level. Usually, the Markovian generator cannot satisfy any Poincaré's inequality. Hence, no Gronwall's lemma can easily lead to the exponential decay of Ft (the L2 norm of a test function along the semi-group). Nevertheless for the kinetic Fokker-Planck dynamics and for a piecewise deterministic evolution we show that Ft satisfies a third order differential inequality which gives an explicit rate of convergence to equilibrium.
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