报告题目：Convergence rates in homogenization of parabolic systems with locally periodic coefficients locally periodic coefficients

报 告 人：徐侥 博士后 中国科学院数学与系统科学研究院数学所

照    片：

邀 请 人：李芳，李善兵

报告时间：2020年10月27日（周二） 9：00-10：00

腾讯会议ID：295 314 322

报告人简介：徐侥，中国科学院数学与系统科学研究院数学所博士后。2019年博士毕业于南京大学，师从钟承奎教授。2016年受国家公派联合培养研究生项目赴美国肯塔基大学留学两年，合作导师为申仲伟教授。目前已在J. Funct. Anal., Comm. Partial Differential Equations， J. Differential Equations, Discrete Contin. Dyn. Syst.等期刊发表学术论文多篇。

报告摘要： This talk mainly concerns with the quantitative homogenization of second-order parabolic systems with time-dependent locally periodic coefficients in $C^{1,1}$ cylinders. Under nearly minimal smoothness assumptions on the coefficients which indicate the 1st order differentiability in $x$ and 1/2+ order differentiability in $t$, the sharp-order scale- invariant convergence rate to some $u_0$ is established. To do this, we employ fractional derivatives on intervals to build several almost optimal estimates for the macroscopic smoothing operator, and derive a new estimate for the integrals on temporal boundary layers.