报告人：林芳华教授（美国纽约大学柯朗研究所）
时 间：2019年6月21日下午 15:30-16:30
地点：华南数学应用与交叉研究中心学术报告厅111
题目： Uniform Boundary Controllability and Homogenization of Wave Equations
摘要：
It has been a long standing problem since early 1980s posed by lateJ.L.Lions that concerning the Uniform Controllability of Wave Equations in highly oscillating (hetrogeneous) medium. The identification of the
limit of (optimal) controls and the (optimal) control for the homogenized limiting problem; as well as counterexamples to uniform controllability were known since late 1980s and early 1990s. In this lecture, I will discuss my recent joint work with Zhongwei Shen on this problem. We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is uniform in ε - the scale of the microstructure, for the projection of solutions to the subspace generated by the eigenfunctions with eigenvalues less that Cε^{−2/3}. I shall discuss also the related eigenvalues and eigenfunctions estimates which are uniform in ε.
报告人简介：
林芳华教授是美国纽约大学柯朗研究所的Julius Silver首席教授，曾于1988-1989和1996-1997任芝加哥大学教授。1989年分别荣获Presidential Young Investigator和Alfred P. Sloan Fellow。1990年，在国际数学家大会上，年仅31岁的林芳华被邀请作大会45分钟学术报告。2002年，荣获美国数学会Bocher奖，2004年获华人数学家大会陈省身奖。2004年被评为美国科学与艺术院院士，并于2015年被评为美国数学会的fellow。
主要研究兴趣包括经典和应用分析，偏微分方程，几何测度论，以及变分运算。著有200多篇学术论文和多本专著：《Elliptic Partial Differential》, 《Geometric Measure theory：An Introduction》 and 《The Analysis Of Harmonic Maps And Their Heat Flows》等。
文件下载：林芳华杰出报告海报6.21.pdf