报告题目：On a competitive system in periodic habitats
时 间：2026年11月13日 (星期五) 10：00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：A competitive system with diffusion and advection in periodic habitats is investigated. The dynamics was understood when both diffusion rates are small or large by Liu and Lou [Methods Appl. Anal., 28 (2021), pp. 423–452] and it was stated there that fully understanding the dynamics is a quite challenging issue. In this paper, we pursue this issue further and obtain much richer results: the global dynamics is determined when one diffusion rate is arbitrarily given and the other one is small or large, when the advection rate is small or large, or when the spatial period is small, improving the existing results in a nontrivial sense. Our main approach is to develop the principal eigenvalue theory. In particular, we establish several new monotonicity results of the principal eigenvalue, where new ingredients are incorporated into the nonlinear analysis of various asymptotic behaviors of positive solutions and principal eigenfunctions.
报告人简介：周鹏，上海师范大学数学系教授，博士生导师。2015年获上海交通大学理学博士。2015-2017年受加拿大北大西洋数学科学研究协会（AARMS）资助从事博士后研究。主持国家自然科学基金优秀青年科学基金项目、面上项目，上海市科委基础研究项目等，入选上海市东方学者特聘教授及跟踪计划。主要研究方向为微分方程与动力系统以及生物数学，围绕无穷维竞争系统全局动力学做出系列工作，部分结果发表在JDE，JFA，JMPA，SIMA，SIAP等国际数学期刊。