A hybrid parabolic and hyperbolic equation model for a population with separate dispersal and stationary stages: well-posedness and population persistence

讲座时间 Datetime: 2022年6月24日，星期五，10:00—11:30

地点 Venue: 腾讯线上会议：199-314-842

主持人 Host：唐德

报告人 Speaker: 黄启华

单位 Affiliation:西南大学

报告摘要 Abstract:

The life cycles of many species include separate dispersal and sedentary stages. To understand the population dynamics of such species, we develop and study a hybrid parabolic and hyperbolic equation model, in which a reaction-diffusion equation governs the random movement and settlement of dispersal individuals, while a first-order hyperbolic equation describes the growth of stationary individuals with age structure. We establish the existence and uniqueness of the solution of the model using the monotone method based on a comparison principle. We study the population persistence criteria in terms of four related measures. We numerically investigate how the interplay between population dispersal, reproduction, settlement, and habitat boundary affects the population persistence.