讲座题目：Uniform Boundary Controllability and Homogenization of Wave Equations 主讲人：林芳华 教授 主持人：周风 教授 开始时间：2019-07-12 16:00:00 结束时间：2019-07-12 17:00:00 讲座地址：中北校区地理楼385报告厅 主办单位：数学科学学院
报告人简介： 林芳华教授1985年美国明尼苏达大学获博士学位。他2004年当选美国艺术与科学院院士，纽约大学Silver教授，纽约大学Courant数学所终身教授。林芳华在几何测度论、偏微分方程、几何分析、变分学、液晶、超流、复杂流体等数学领域都做出了突出的贡献,在数学界影响深远。他著有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》。三十年来，他为推动发展中国的数学事业、培养数学人才，做出了巨大努力。他所获荣誉包括：1990年在国际数学家大会上作45分钟特邀报告。2002年获美国数学会Bocher奖（这是每5年颁发一次的专门奖励分析学科重要成就的奖项）、2004年获华人数学家大会陈省身奖。 报告内容： It has been a long standing problem since early 1980s posed by the late J.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 theuniform 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 the sharp convergence rate 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. |
