报告人：吴启亮（俄亥俄大学）

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

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.

报告时间：2024年11月7日（星期四）10:00-12:00

                 2024年11月8日（星期五）10:00-12:00

报告地点：科技楼南705室

邀请人：李骥