报告题目：Measure Differential Equations (MDE): Absolutely Continuous (ac) Measures vs Completely Singular (cs) Measures
报 告 人：章梅荣 教授 (清华大学)
报告时间：2018年7月17日（周二）下午16:00-17:00
报告地点：数学楼425学术报告厅
摘要：Measure Differential Equations (MDE) can be considered as the limiting case of the usual Differential Equations. In this talk, by taking the spatial oscillation of 1D strings with general distributions of masses as an example, we will discuss how solutions and eigenvalues of MDE depend on measures in MDE. As a consequence of the so-called completely continuous dependence, we will show that ODEs and Algebraic Equations (AEs) can be mutually approximated, including their solutions, eigenvalues, etc. These results may be used to solve some applied problems, and even to yield some numerical methods for finding eigenvalues. .
个人简介：章梅荣, 清华大学数学科学系教授、兼任清华大学周培源应用数学研究中心副主任，2003年的国家杰出青年科学基金获得者，先后获得“茅以升北京青年科技奖”、教育部“高校青年教师奖”等奖励。章教授主要从事动力系统理论研究，在动力系统、非线性振动、非线性分析等研究领域等方面已经发表论文80多篇，其中被SCI收录的有70多篇。主要成果包括:离散双曲系统的共轭分类结果，发展了"嵌入流"方法，拓广了特征值和谱的旋转数方法，阐述了低自由度Lagrange系统的周期运动的扭转性和稳定性，并在奇异系统的周期边值问题等方面取得重要结果。
