Dynamics of a reaction-diffusion system with time-periodic and spatially dependent delay: A quotient space approach

讲座题目：Dynamics of a reaction-diffusion system with time-periodic and spatially dependent delay: A quotient space approach
讲座时间 Datetime: 2025年5月10日，周六，09:00-12:30
地点 Venue: 中大珠海校区海琴二号A457
主持人 Host：易泰山 教授
报告人 Speaker: 楼一均 教授
单位 Affiliation: 香港理工大学
报告摘要 Abstract:
Understanding the impact of temporal and spatial heterogeneity  on population dynamics has significantly advanced mathematical theories in reaction-diffusion systems. This talk reports the global dynamics of a   reaction-diffusion system with time delay, where all model parameters are spatially and temporally dependent. The main focus lie in threefold: (i) formulating a stage-structured model that incorporates diffusion and temporally and spatially inhomogeneous development delay; (ii) proposing a dynamical systems framework that employs a quotient phase space to establish strong monotonicity of the periodic semiflow; (iii) establishing a threshold-type result under minimal assumptions, for both increasing and unimodal birth functions. This synthesized approach is expected to motivate further studies when strong monotonicity of the solution semiflow fails in conventional phase spaces.
报告人简介：
楼一均，现任香港理工大学副教授。主要研究方向为应用动力系统及其在复杂生物系统的应用。论文发表在SIAM JAM, SIAM JCO, IEEE TAC, SIAM JADS, JNS, Nonlinearity, JDE, JMB, Chaos, BMB, JTB等主流应用数学以及理论生态学杂志。在国际期刊上发表论文70 余篇，引用次数超7700次。现任Infectious Disease Modelling杂志Associated Editor(执行编委)，以及Advances in Continuous and Discrete Models等六个期刊编委会成员。近期研究受国家自然科学基金面上项目和香港特别行政区大学教育资助委员会资助。同时担任香港理工大学科技应用数学理学硕士项目课程主任。