Report Title：Traveling Waves for Burgers-Fisher-KPP Equations with Singularity
Reporter：Professor Mei Ming
Affiliation: McGill University & Champlain College, Canada
Report Time:9:30-10:30 June 25,2026
Report Location:Tencent Meeting ID: 428-514-010
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https://meeting.tencent.com/dm/MWJ6vE88RB1j
University Contact: Liu Changchun (liucc@jlu.edu.cn)
Abstract:
In this talk, I will present a recent study on Burgers-Fisher-KPP equation with singular slow/fast diffusion and singular/regular convection in the form of $u_t-D\Delta u^m+\alpha(u^p)_x=f(u)$ with $m,\,p>0$, focusing on the existence, non-existence, regularity and stability of traveling waves. The values of m and p essentially affect the existence/non-existence of regular/sharp traveling waves as well as their regularity. By combining phase-plane analysis and variational techniques, we obtain a complete classification of existence/non-existence of regular/sharp traveling waves related to m and p. In the singular regimes with 0<p<1 or 0<m<1, where the convection or diffusion exhibit strong singularity at u=0, we introduce a change of variables to overcome the singularity, thereby deriving existence/non-existence results characterized by the minimal convection coefficient. Finally, for the case of slow diffusion $m>1$ with convex convection p>1, we prove the stability of non-critical traveling waves via $L^1$-weighted energy method. This is a joint work with Zhuangzhuang Wang, Rui Huang, Zejia Wang and Wenhuan Liang.
Bio:
Mei Ming is an Adjunct Professor at McGill University in Canada, a Tenured Professor at Chambord College in Canada, a Distinguished Professor at Jiangxi Normal University, a Foreign Senior Scholar of the National Science Foundation (formerly known as "Overseas Outstanding Young Scholar"), an Overseas High-end Talent of the Ministry of Science and Technology, a Foreign Senior Scholar of the Japan Society for the Promotion of Science (JSPS), and ranked among the top 0.98% of the world's top scientists for 2024 according to ScholarGPS, an international academic institution. She primarily focuses on research in the qualitative analysis of solutions to Navier-Stokes equations, Euler equations, Euler-Poisson equations, and delay reaction-diffusion equations. She has published over 140 papers in top academic journals such as ARMA, SIMA, and M3AS, and is listed as a top author for SIMA and JDE by American Mathematical Reviews. Four of her papers are ESI Highly Cited Papers. She serves as an editorial board member for four SCI international journals, including Applicable Analysis, and has been a reviewer for the Scientific Exploration Award.
