Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Charles Collot, CY Cergy Paris Université
Inviter:	Xiangdi Huang and Quoc Hung Nguyen
Title:	Description of singularity formation for Burgers, Prandtl and Keller-Segel equations：Preliminaries on the parabolic-elliptic Keller-Segel system (3)
Language:	Chinese
Time & Venue:	2023.07.12 10:00-11:00 思源楼S813
Abstract:	These lectures will concern the qualitative study of some evolution partial differential equations modelling advection, diffusion and reaction. The Burgers and Prandtl equations describe fluid flows, and the Keller-Segel system bacteria motion. We will focus on singularity formation, and will describe precisely mathematically the associated concentration patterns. A common mathematical phenomenon will be observed: the solution is to leading order self-similar. We will first describe how self-similarity occurs for shocks in transport equations, with an approach that differs from the usual geometric one of John, Alinhac, Christodoulou and others. This will be achieved via the use of representation formulas given by characteristics based on joint works from the author with Ghoul, Ibrahim, Lin and Masmoudi. The stability of self-similar singularity formation will then be addressed for the Keller-Segel system. This will rely on a spectral approach, and will be based on recent works of Glogic and Schorkhuber, and from the author with Ghoul, Masmoudi, Merle, Nguyen and Raphael.