时间：2024年12月11日上午10:00-11:00

地点：数学楼2-3会议室

报告人：聂华 教授（陕西师范大学）

题目: Dynamics analysis of a reaction-diffusion-advection benthic-drift model with logistic growth
摘要: The purpose of this paper is to investigate the benthic-drift population model in both open and closed advective environments, focusing on the logistic growth of benthic populations. We employ the theory of monotone dynamical systems to analyze the threshold dynamics. Specifically, when the zero solution is linearly unstable, we first obtain upper and lower semi-continuous limits by iterating monotonically from upper and lower solutions. Then, using a part metric, we prove that these two limits are equal and continuous, enabling us to construct a positive steady state. Furthermore, we conduct a quantitative analysis of the principal eigenvalue for a non-self-adjoint eigenvalue problem to examine how the diffusion rate, advection rate, and population release rates influence the dynamics. The results suggest that the diffusion rate and advection rate have distinct effects on population dynamics in open and closed advective environments, depending on the population release rates.

简介：聂华，教授、博士生导师，研究方向：反应扩散方程与空间生态种群模型。现任中国数学会生物数学专业委员会委员、中国数学会计算数学分会理事。2006年于陕西师范大学获得博士学位；入选教育部“新世纪优秀人才支持计划”和陕西省“青年科技新星”，获得陕西省杰出青年基金；多次赴美国明尼苏达大学、澳大利亚新英格兰大学、台湾清华大学合作研究与访问。已主持国家自然科学基金面上项目3项，主持完成省部级项目3项；已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“SIAM J. Appl. Dyn. Syst.”、“J. Differential Equations”、“J. Math. Biol.”、“Math. Biosci.”、“European J. Appl. Math.”、“Proc. London Math. Soc.”、“Sci. China Math.”等国内外知名刊物上发表学术论文70多篇。