报告题目：Dynamics analysis of a reaction-diffusion-advection benthic-drift model with logistic growth

报告人：聂华

报告时间：2024年11月10日（周日）上午09:00开始

报告地点：数学楼315会议室

报告摘要：The purpose of this talk is to investigate the benthic-drift population model in open and closed advective environments, focusing on the logistic growth of benthic populations. We employ the theory of monotone dynamical systems to establish the threshold dynamics. In special, when the zero solution is linearly unstable, we first obtain upper and lower semi-continuous limits separately by monotonically iterating from upper and lower solutions; then using a part metric, we prove that these two limits are equal and continuous in order to construct a positive steady state. Furthermore, we conduct a quantitative analysis of the principal eigenvalue for a non-self-adjoint eigenvalue problem to study the impact of diffusion rate, advective rate, and population release rates on the dynamics. The results suggest that the diffusion rate and advection rate play distinct roles for different population release rates in open and closed advective environments, respectively.

报告人简介：聂华，陕西师范大学教授、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。