On a Dispersive Model for the Unzipping of Double-Stranded Dna Molecules

Abstract

The paper deals with the analysis of a nonlinear Fokker–Planck equation modeling the mechanical unzipping of double-stranded DNA under the influence of an applied force. The dependent variable is the probability density of unzipping m base pairs. The nonlinear Fokker–Planck equation we propose here is obtained when we couple the model proposed in [D. K. Lubensky and D. R. Nelson, Pulling pinned polymers and unzipping DNA, Phys. Rev. Lett.85 (2000) 1572–1575] with a transcendental equation for the applied force. The resulting model incorporates nonlinear effects in a different way than the usual models in kinetic theory. We show the well-posedness of this model. For that we require a combination of techniques coming from second-order kinetic equations and compensated compactness arguments in conservation laws.