Abstract: The purpose of this talk is to examine the stability of shock waves for the viscous Burgers equation in the presence of a boundary. I will first provide a general introduction to the motivation behind investigating the stability of partial differential equations (PDEs). After that, I will focus on the stability analysis of shock waves on a half-line, specifically for cases where the wave is either moving toward or away from the boundary. By employing an approach based on Green’s functions, we establish pointwise estimates to demonstrate their stability. This talk is based on joint work with Shih-Hsien Yu. 

 

Organizers: Harry Richman (NCTS), Wille Liu (Academia Sinica)