Mini-Course：Orbital stability of propagated waves in parabolic systems

报 告 人：Louis Garénaux (KIT, 卡尔斯鲁厄理工学院)

报告时间：2025年12月2日（星期二）10:00—11:30；2025年12月9日（星期二）10:00—11:30

报告地点：数学科学学院114（小报告厅）      

校内联系人：廖娴 教授         联系方式：84708351-8501

Abstract: In these two lectures, we will discuss a class of partial differential equations that models a large range of biological and physical phenomena. Some of their solutions are given as a fixed profile traveling with constant speed.

We will discuss the long time stability of these specific solutions. Due to translational invariance, the linearized dynamics spectrum touches the imaginary axis. As a consequence, it is necessary to distinguish between shape and phase dynamics. I will present the different tools and approaches that where developed in the past fifty years to separate and control these different dynamics. If time allows, we will discuss possible extensions of these tools to open problems.