Academic Report of School of Mathematical Sciences [2026] No. 049

(Series Report for High-Level University Construction No. 1308)

Title：Boundedness and long-time behavior of solutions to some chemotaxis models

Speaker：Chia-Yu Hsieh, Associate Professor (Sun Yat-sen University Zhuhai Campus)

Time：14:40-15:40, May. 22, 2026

Location：Huixing Building Room501, Yuehai Campus

Abstract：In this talk, I will first discuss the boundedness and long-time behavior of solutions to the parabolic-elliptic Keller-Segel equation, which is a basic model for chemotaxis. It is well known that solutions may exist globally or blow up in finite time, depending on initial data. In two dimensions, using a scaling and translation argument, we show that solutions with subcritical mass have a temporal decay estimate. By further considering the limiting flow, long-time behavior of solutions can be characterized under self-similar variables. Similar results in higher dimensions can be obtained under smallness assumptions. The argument can be applied to an attraction-repulsion model in two dimensions, and we obtain the uniform boundedness of solutions with subcritical mass. This talk is based on joint works with Yong Yu at the Chinese University of Hong Kong.

Speaker Profile：Chia-Yu Hsieh is currently an associate professor at School of Mathematics (Zhuhai), Sun Yat-sen University. He obtained his Ph.D. degree in Mathematics from National Taiwan University. Afterwards, he held postdoctoral positions at City University of Hong Kong, National Center for Theoretical Science in Taiwan, and the Chinese University of Hong Kong. His research focuses on analysis of partial differential equations, with applications including ionic transport and chemotaxis.

Faculty and students are welcome to attend!

Invited by: Qingtian Zhang

School of Mathematical Sciences

May 18, 2026