Singularity effects for advection-diffusion equations with fast / slow diffusion

2025西安電子科技大學(xué)

非線性分析、微分方程與動力系統(tǒng)系列報告

本期組織：吳事良、薄偉健

主辦單位：西安電子科技大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院

基金資助：國家自然科學(xué)基金、陜西省杰出青年科學(xué)基金

報告信息

(以姓氏拼音為序)

Singularity effects for advection-diffusion equations with fast/slow diffusion

Ming Mei(梅茗) McGill University and Champlain College

摘要：This talk is a survey of our recent studies on Fisher-KPP equations and Burgers equations with fast/slow diffusion with singularities. When the diffusion is degenerate with singular point u=0, the equations possess the so-called sharp traveling waves which are regionally degenerate. On the other hand, when the diffusion is fast diffusion, the equations become singular at u=0. The main concerns of this talk are to investigate the sharp traveling waves and their stabilities. Singularities for both the fast/slow diffusion cases cause the essential difficulty for the study.

報告人簡介：梅茗，加拿大麥吉爾大學(xué)的Adjunct Professor,加拿大尚布蘭學(xué)院的終身教授，江西師范大學(xué)特聘教授，日本文部省JSPS外國資深學(xué)者，國際學(xué)術(shù)機構(gòu) ScholarGPS發(fā)布的2024全球頂尖科學(xué)家排名前0.98%。主要從事Navier-Stokes方程、歐拉方程、歐拉-泊松方程、時滯反應(yīng)擴散方程解的定性分析等方面的研究，在ARMA，SIMA， CPDE，M3AS等一流學(xué)術(shù)刊物發(fā)表論文140余篇，H-index為34，被《美國數(shù)學(xué)評論》列為SIMA及JDE的top authors,有4篇論文是ESI 的高被引論文。是《Applicable Analysis》等4個SCI國際期刊的編委，也一直是“科學(xué)探索獎”海外評審專家之一。