弱空间约束下非因式分解动力学Fokker-Planck方程的李雅普诺夫估计
Lyapunov estimates for non-factorised kinetic Fokker-Planck equations under weak spatial confinements
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中文总结 AI 辅助
本文针对带弱外部约束的非因式分解动力学Fokker-Planck方程，构造弱李雅普诺夫泛函，运用Harris型论证证明其稳态存在性及显式拉伸指数收敛速率。
中文摘要 AI 辅助
本文针对带有弱外部约束的动力学Fokker-Planck方程构造了弱李雅普诺夫泛函，该问题在现有文献中仍广泛未解决。除揭示模型的有趣结构外，推导这些Foster-Lyapunov权重使我们能运用Harris型论证证明这些方程的稳态存在性，并以显式拉伸指数速率收敛到平衡态。
英文摘要
In this paper, we construct weak Lyapunov functionals for kinetic Fokker-Planck equations with weak external confinements. This problem has remained widely open in the existing literature. Apart from showing interesting structures from the models, deriving these Foster-Lyapunov weights allows us to use Harris type arguments to show existence of steady states for these equations, and convergence to equilibrium with an explicit stretched exponential rate.
