Transport Models for Collective Dynamics in Biological Systems

Entropy satisfying methods for Fokker-Planck-type equations

Hailiang Liu

Iowa State University

Kinetic Fokker-Planck equations have been widely used to study statistical effects of various complex dynamics. In such models, the entropy structure is the main mechanism for the underlying distribution to evolve into some stable equilibrium patterns. In this talk I’ll recount progress toward understanding the role of the entropy in the design of numerical methods to capture the long-time behavior. The present schemes are shown to satisfy three important properties: (i) mass conservation, ii) positivity preserving; and iii) entropy satisfying. These ensure that the schemes provide a satisfying long-time behavior, thus underline the efficiency to preserve the large-time asymptotic. Applications include the FENE dumbbell model in polymeric fluids, and biological dispersal in population dynamics.