系列报告题目：Nonlinear Stability of Periodic Patterns

报告题目1：Existence of spatially periodic patterns and its defects in the Swift-Hohenberg equation

报告人：吴启亮教授，美国俄亥俄大学

报告时间：2024年10月24日（周四）15:00-16:00

报告地点：20-200

报告摘要：Pattern formation, arising ubiquitously in biological, chemical and physical systems, has been an active research area for over a century. Among others, the existence and stability of patterns and their defects in pattern forming systems have been always one of the fundamental topics. In this talk, we would like to introduce some basic tools, that is, Lyapunov-Schmidt reduction and central manifold theorem, via the study of existence of spatially periodic patterns and its defects in the Swift-Hohenberg (SH) equation. More specifically, we would like to use the existence of spatially periodic patterns in the SH equation to showcase the application of the Lyapunov-Schmidt method and the existence of one of the defects, that is, grain boundaries, to showcase the application of the central manifold theorem, which, in combination with spatial dynamics, normal form theory and implicit function theorem, is a powerful tool in the field of nonlinear dynamics and pattern formation.

报告人简介：吴启亮，美国俄亥俄大学教授，研究领域为非线性动力系统微分方程，生物数学。本科毕业于中国科技大学，2013年于美国明尼苏达大学获博士学位，后于密歇根州立大学作博士后研究。其研究获美国国家自然科学基金资助。在JDE，JMPA，JMB，PRSE等国际权威杂志发表论文数十篇。