报告题目：Traveling Waves for Burgers-Fisher-KPP Equations with Singularity

报告人：梅茗 教授 McGill University & Champlain College 加拿大

报告时间：2025年10月23日  8:30-9:30

报告地点：腾讯会议 ID：621-584-582

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校内联系人：刘长春 [email protected]

报告摘要：

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.

报告人简介：

梅茗，加拿大麦吉尔大学的Adjunct Professor，加拿大尚布兰学院的终身教授，江西师范大学特聘教授，国家基金委外国资深学者（原“海外杰青”），科技部海外高端人才，日本文部省JSPS外国资深学者，国际学术机构 ScholarGPS 发布的2024全球顶尖科学家排名前0.98%。主要从事Navier-Stokes方程、欧拉方程、欧拉-泊松方程、时滞反应扩散方程解的定性分析等方面的研究，在ARMA, SIMA, M3AS等一流学术刊物发表论文140 余篇，被《美国数学评论》列为SIMA及JDE的top authors,有4 篇论文是ESI 的高被引论文。是《Applicable Analysis》等4个SCI 国际期刊的编委，也一直是“科学探索奖”评审专家之一。