Asymptotic Analysis of Kinetic Models of Collective Behavior

In this dissertation, we study the long-time behavior of the solutions of some kinetic equations arising from the studies of collective behavior. Propagation of chaos is a fundamental question in kinetic theory which enables the reduction of an N-particle description to a single partial differential equation. In Chapter 1, we prove the propagation of chaos for the classical Cucker-Smale system and its variant in which the system is additionally forced with Rayleightype friction and self-propulsion force. Moreover, the quantitative estimates of the rate of the convergence in Wasserstein-2 distance are shown. In Chapter 2, a continuous model of opinion dynamics is considered. The global well-posedness, the regularity, and asymptotic behavior of the solution are studied. In Chapter 3, we investigate the long-time behavior of the solution of a kinetic Fokker-Planck-type equation. The exponential relaxation of the solution to its equilibrium is proved here.