國立清華大學 數學系

Abstract In this talk, we shall give a complete account of the theory on the synchronization issues for the Kuramoto oscillators with inertia effect. Both the frequency synchronization and phase synchronization are in view. The crux of analysis on this problem is due to the collisions and the lack of the uniform boundedness of the initial velocity. We shall do some nonlocal estimates on the speed functions to give good estimates on the diameter function to overcome the aforementioned crux. This is joint work with Bongsuk Kwon and Chang-Yeol Jung.