Academic Report of School of Mathematical Sciences [2026] No. 040

(Series Report for High-Level University Construction No. 1299)

Title：Spike solitons and weak solutions of the mCH equation

Speaker：Yu Gao (Harbin Institute of Technology, Shenzhen)

Time：10:30-11:30, May. 11, 2026

Location：Huixing Building Room 501

Abstract：This report addresses the well-posedness problem for two classes of weak solutions to the mCH equation. One class consists of traditional weak solutions defined using test functions; however, these solutions do not guarantee energy conservation or dissipation. The other class consists of energy-conserving weak solutions that include a singular product term (the product of the Radon measure and the BV function). For traditional weak solutions, we will present two methods for finding spiky soliton solutions to the mCH equation, as well as the mean-field limit method for finding general weak solutions; finally, we will introduce the viscous particle method for finding energy-conserving spiky soliton solutions.

Speaker Profile：Yu Gao received his Ph.D. from Harbin Institute of Technology in 2018. He subsequently worked at the University of Hong Kong and the Hong Kong Polytechnic University before joining the School of Science at Harbin Institute of Technology (Shenzhen) in 2024. His current research focuses on the well-posedness theory of solutions to partial differential equations, including the global existence and uniqueness of weak solutions, the stability of particular solutions, and the asymptotic behavior of integrable equations such as the Camassa-Holm and Hunter-Saxton equations. His research findings have been published in journals such as CVPDE, SIMA, and JDE.

Faculty and students are welcome to attend!

Invited by: Qingtian Zhang

School of Mathematical Sciences

May 8, 2026