报告摘要: This paper aims to investigate the benthic-drift population model in both open and closed advective environments, focusing on the logistic growth of benthic populations. We obtain the threshold dynamics using the monotone iteration method, and show that the zero solution is globally attractive straightforward when linearly stable. When unstable, limits from monotonic iteration of upper and lower solutions are upper and lower semi-continuous, respectively. By employing a part metric, we prove these limits are equal and continuous, leading to a positive steady state. In the critical case, we establish that the limit function from the upper solution iteration must be the zero solution by analyzing an algebraic equation. 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.

报告时间：2024年12月18日（周三）上午9:00-10:30

报告地点：线上，腾讯会议：765-734-867

报告人简介：

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；入选国家级和省级人才计划，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。