论文标题
半平面中半灵聚合物的动力学模型
Kinetic Models for Semiflexible Polymers in a Half-plane
论文作者
论文摘要
基于半辅助聚合物链的一般离散模型，我们通过连续性极限引入了半平面中半平面聚合物的动力学方程的形式推导。事实证明，在非局部捕获边界条件下，所得方程是具有Laplace-Beltrami操作员的动力学Fokker-Planck-type方程。然后，我们研究了所得方程溶液的拟合良好和长链渐近学。特别是，我们证明存在一个针对相应边界值问题的唯一测量值解决方案。此外，我们证明了方程是低纤维化的，并且溶液在奇异边界附近是局部连续的。最后，我们为大型聚合物链提供了溶液的渐近行为。
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.
