1. Time: April 14th (Monday) 10:00
Place: Natural Science Building #744
Speaker: Dr. Jaeyoung Yoon (Technical University of Munich)

Title: Adaptive Cucker-Smale Model and its Asymptotic Behavior in the Singular Limit

Abstract:
In this talk, we introduce an adaptive network within Cucker-Smale (CS) dynamics. The properties of adaptive networks allow particles in the CS regime to form and break up groups of neighbors, resulting in the emergence of diverse patterns. We investigate the singular limit of the adaptive CS model to better understand the role of the adaptive rule, which transforms the system into Laplacian dynamics on a temporal graph. Through the analysis of Laplacian dynamics on various types of temporal graphs, we demonstrate the asymptotic behavior of the adaptive CS model in this singular limit.

2. Time: April 14th (Monday) 11:00
Place: Natural Science Building #744
Speaker: Youngseok Yoo (Yonsei University)

Title: Existence and Large-time behavior of the solutions for the nonlinear Vlasov-Poisson-Fokker-Planck Equation

Abstract:
The Vlasov equation models collisionless systems with long-range interactions, such as plasmas or galaxies, while the Fokker-Planck equation accounts for random forces including thermal fluctuations, collisions, and noise. The Vlasov-Fokker-Planck equation describes the evolution of a particle distribution function in phase space under the influence of self-consistent forces, external potentials, and diffusive effects. This framework is fundamental in fields such as plasma physics, kinetic theory, and statistical mechanics. In this talk, we focus on the nonlinear Vlasov-Poisson-Fokker-Planck equation, where the force arises from self-consistent interactions, meaning that the particles generate a field that, in turn, acts back on the system. We study the existence and large-time behavior of solutions to this equation in the whole space. We first establish the local existence and uniqueness of solutions for suitably regular initial data. These results are then extended to global existence through the use of energy estimates and macro-micro decomposition techniques. Finally, we analyze the long-time behavior of solutions, demonstrating algebraic decay toward equilibrium under appropriate conditions.