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 Laplace–Beltrami operator under a nonlocal
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.
