On impulsive reaction-diffusion-advection models in higher dimensions-数学学院
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On impulsive reaction-diffusion-advection models in higher dimensions

发布时间:2018年06月11日 15:22   浏览次数:
报告人 Hao Wang 年月 2018-06
13

报告题目: On impulsive reaction-diffusion-advection models in higher dimensions

报告人:Hao Wang 

报告人单位:University of Alberta

报告时间:613日(周三)下午14:00-15:00

报告地点:数学学院东409报告厅 

邀请人:邹兰

 

摘要:

We formulate a general impulsive reaction-diffusion-advection equation model to describe the population dynamics of species with distinct reproductive and dispersal stages. The seasonal reproduction is modeled by a discrete-time map, while the dispersal is modeled by a reaction-diffusion-advection partial differential equation. Study of this model requires a simultaneous analysis of the differential equation and the recurrence relation. When boundary conditions are hostile we provide critical domain results showing how extinction versus persistence of the species arises, depending on the size and geometry of the domain. We show that there exists an extreme volume size such that if the region size falls below this size the species is driven extinct, regardless of the geometry of the domain. To construct such extreme volume sizes and critical domain sizes, we apply the classical Rayleigh-Faber-Krahn inequality and the spectrum of uniformly elliptic operators. The critical domain results provide qualitative insight regarding long-term dynamics for the model. Last, we provide applications of our main results to certain biological reaction-diffusion models regarding marine reserve, terrestrial reserve, insect pest outbreak, and population subject to climate change.

*This is a joint work with Mostafa Fazly (University of Texas at San Antonio) and Mark A. Lewis (University of Alberta).

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