数学系学术报告
微分方程与动力系统系列报告
报告题目：Pulses in pattern-forming systems with strongly localized inhomogeneities
报告人： 李骥 教授
报告时间：2026/10/01 （周四） 16:00-17:00
报告摘要：Spatially localized structures, such as spikes and pulses, constitute fundamental coherent states in a broad class of pattern-forming systems. These localized patterns arise in diverse physical, chemical, and biological settings. In realistic physical and biological systems, the media supporting pattern formation are rarely homogeneous. Such heterogeneities, whether arising intrinsically within the medium or imposed externally, can strongly affect both the emergence and the stability properties of localized structures. We explain how geometric singular perturbation theory along with matched asymptotic expansion can be used to study a general kind of strongly localized inhomogeneity, providing existence and stability conditions in terms of algebraic equations. We also provide mechanism of stable multi-front/back/pulse, as well as stable non-monotone fronts.
报告人简介：李骥，华中科技大学数学与统计学院教授，博士生导师。2008年本科毕业于南开大学数学试点班，2012年在美国杨伯翰大学取得博士学位，后在明尼苏达大学和密西根州立大学做博士后及访问助理教授，2016年加入华中科技大学。主要研究两类问题：1.几何奇异摄动理论及其在尤其是反应扩散方程组中的应用，尤其是行波的存在性，稳定性，以及其分支和相关动力学行为；2.浅水波孤立子稳定性问题，尤其是一类拟线性的浅水波孤立子问题。在包括TAMS , JMPA，JFA，AnnPDE，JDE，PhyD等杂志发表论文三十多篇。