Workshop on the homogenization problems
会议时间和地点：10月15日，理1303
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时间
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报告人
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题目
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9:00-10:00
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耿俊
（兰州大学）
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Elliptic Problems and Periodic Homogenization on Non-smooth Domains
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10:00-10:30
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休息、讨论
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10:30-11:30
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荆文甲
（清华大学）
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Homogenization of Hamilton-Jacobi equations in dynamic random environments
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中午
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休息
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14:30-15:30
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吕勇
（南开大学）
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Homogenization problems in fluid mechanics
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15:30-16:00
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休息、讨论
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16:00-17:00
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徐强
（welcome欢迎光临威尼斯公司）
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Convergence rates for elliptic homogenization problems
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报告题目及摘要
Elliptic Problems and Periodic Homogenization on Non-smooth Domains
耿俊（兰州大学）
In this talk I will introduce some recent results for boundary value problem of elliptic equations on non-smooth domains. Also, I will discuss recent progress on uniform estimates for elliptic/parabolic homogenization.
Homogenization of Hamilton-Jacobi equations in dynamic random environments
荆文甲（清华大学）
I will present some recent results on the qualitative homogenization theory for Hamilton-Jacobi equations in dynamic environments. Such equations find applications in the modeling of front propagation and in optimal control theory when the underlying environment is time dependent and highly oscillatory. The goal of homogenization is to determine effective environment that is non-oscillatory but characterizes the averaged effect of the oscillatory environment on the equation. Though the homogenization theory of Hamilton-Jacobi equation is well studied for static environments, some difficulty persists in the dynamic setting due to the lack of uniform Lipschitz controls of the solutions. The presented results, albeit being partial, provide new unified approaches for qualitative stochastic homogenization. This talk is based on joint works with P.E. Souganidis and H.V. Tran.
Homogenization problems in fluid mechanics
吕勇（南开大学）
I will talk about homogenization problems in fluid mechanics --- the study of asymptotic behavior of fluid flows (governed by Stokes, Navier-Stokes or Euler equations) in domains perforated with a large number of tiny holes (obstacles).
With an increasing number of holes, the fluid flow approaches an effective state governed by certain ”homogenized” equations which are homogeneous in form (without holes). The homogenized equation (or limit equation) is crucially determined by the ratio between the size of the holes and the mutual distance of the holes.
In this talk, I will introduce the background of this study and some known results. I will also recall my recent results in this research field. At the end, I will present some open problems.
Convergence rates for elliptic homogenization problems
徐强（welcome欢迎光临威尼斯公司）
这次报告的主题是椭圆均匀化理论中关于收敛速度的估计。首先回顾近几年该领域的几个重要结果和重要方法。然后介绍几个加权不等式，对偶方法，层及于层类型的估计。以上数学工具可以得到均匀化问题在Lipschtiz区域上的几乎最佳的收敛速率。
