数学系--偏微分方程中心联合讨论班
Department of Mathematics- Center for PDE
Joint Seminar
报告题目: Asymptotics of the interface of a Hele-Shaw flow with multiple point sources
演讲人： Dr. Michiaki Onodera
National Taiwan University
时间： 2011年3月15日（星期二）下午1:00—2:00
地点： 华东师大闵行校区数学系102报告厅
摘要
We study the asymptotic behavior of the interface of a Hele-Shaw flow produced by the injection of fluid from finitely many points at different speeds. We prove that, as time goes to infinity, the interface approaches an expanding circle centered at the barycenter of the injection points with weights proportional to the injection rates. The distances from the barycenter to the boundary points are estimated from above and below. The proof is based on a precise estimate of quadrature domains of the measure in the case where a, b>0 and a+b is sufficiently large. Here denote the Dirac measures at i, -i respectively. The definition and basic ideas of quadrature domains will be provided in the talk. Combining an induction argument with the estimate yields the result
