Gradient flow techniques and applications to collective dynamics

Series: 
PDE Seminar
Tuesday, January 24, 2017 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
UT-Austin
,  
Organizer: 
I will discuss applications of the theory of gradient flows to the dynamics of evolution equations.  First, I will review how to obtain convergence rates towards equilibrium in the strictly convex case. Second, I will introduce a technique developed in collaboration with Moon-Jin Kang that allows one to obtain convergence rates towards equilibrium in some situations where convexity is not available. Finally, I will describe how these techniques were useful in the study of the dynamics of homogeneous Vicsek model and the Kuramoto-Sakaguchi equation. The contributions on the Kuramoto-Sakaguchi equation are based on a joint work with Seung-Yeal Ha, Young-Heon Kim, and Jinyeong Park. The contributions to the Vicsek model are based on works in collaboration with Alessio Figalli and Moon-Jin Kang.