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Kinetic models for semiflexible polymers in a half-plane

Jin Woo Jang and Juan J. L. Velázquez

Vol. 5 (2023), No. 1, 145–212
Abstract

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.

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Keywords
semiflexible polymers, Markov process, Fokker–Planck equation, hypoellipticity, long-chain asymptotics
Mathematical Subject Classification
Primary: 82D60, 82C31, 46N55, 92C45
Milestones
Received: 18 January 2022
Revised: 18 June 2022
Accepted: 24 July 2022
Published: 24 April 2023
Authors
Jin Woo Jang
Department of Mathematics
Pohang University of Science and Technology (POSTECH)
Pohang
South Korea
Juan J. L. Velázquez
Institute for Applied Mathematics
University of Bonn
Bonn
Germany