Aggregation equations over bounded domains
Expositor: Weiran Sun
Instituição: Simon Frasier University
Data e Horário: 15/04/19 | 16:00h

RESUMO: Numerical computations have shown that due to the boundary effect, solutions of aggregation equations can evolve into non-energy minimizing states. Meanwhile, adding a small noise seems to bypass such non-energy minimizers. This motivates our study of aggregation equations over bounded domains. In this talk we will use basic probabilistic methods to show well-posedness and mean-field limits of aggregation equations with singular potentials (such as the Newtonian potential). We will also show the zero-diffusion limit of aggregations equations over bounded domains and obtain a convergence rate that is consistent with what has been observed in numerical simulations. This is joint work with Razvan Fetecau, Hui Huang, and Daniel Messenger