AI 中文总结
该研究针对非微扰情形下带多孔介质扩散的非线性动力学Fokker–Planck方程，结合熵-熵耗散结构与L²-次协性技术，证明其在宏观量先验条件界下可在L¹中指数收敛到平衡态。
AI 中文摘要
我们研究非微扰情形下带多孔介质扩散的非线性动力学Fokker–Planck方程的长时间行为，在宏观量的先验条件界下，证明其在L¹中指数收敛到平衡态；若初值被限制在两个全局平衡剖面之间，这些界自动满足，该方法结合了熵-熵耗散结构与部分L²-次协性技术。
英文摘要
We investigate the long-time behaviour of nonlinear kinetic Fokker--Planck equations with porous medium diffusion in a non-perturbative setting. Under a priori conditional bounds on macroscopic quantities, we establish exponential convergence to equilibrium in $L^1$. These bounds are automatically satisfied if the initial data is trapped between two global equilibrium profiles. Our approach combines the entropy-entropy dissipation structure and some techniques from $L^2$-hypocoercivity.
Comments14 pages
