半平面中半柔性聚合物的动力学模型
Kinetic Models for Semiflexible Polymers in a Half-plane
AI总结：
本文由半柔性聚合物离散模型经连续介质极限导出带非局部俘获边界条件的 Fokker–Planck 型动力学方程，并证明其测度值解唯一、亚椭圆性、边界附近 Hölder 连续性及长链渐近行为。
摘要：
基于半柔性聚合物链的一般离散模型，我们通过连续介质极限，对半平面中半柔性聚合物的动力学方程进行了形式化推导。结果表明，所得方程是在非局部俘获边界条件下、带有 Laplace–Beltrami 算子的 Fokker–Planck 型动力学方程。随后，我们研究所得方程解的适定性与长链渐近性。特别地，我们证明相应边值问题存在唯一的测度值解。此外，我们证明该方程具有亚椭圆性，且解在奇异边界附近局部 Hölder 连续。最后，我们给出了聚合物链较长时解的渐近行为。
英文摘要：
Based on a general discrete model for a semiflexible polymer chain, we introduce a formal derivation of a kinetic equation for semiflexible polymers in the half-plane via a continuum limit. It turns out that the resulting equation is the kinetic Fokker-Planck-type equation with the Laplace-Beltrami operator under a non-local trapping boundary condition. We then study the well-posedness and the long-chain asymptotics of the solutions of the resulting equation. In particular, we prove that there exists a unique measure-valued solution for the corresponding boundary value problem. In addition, we prove that the equation is hypoelliptic and the solutions are locally Hölder continuous near the singular boundary. Finally, we provide the asymptotic behaviors of the solutions for large polymer chains.
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