高维脉冲反应扩散对流模型

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报告题目:高维脉冲反应扩散对流模型

(On impulsive reaction-diffusion-advection models in higher dimensions)

报告365bet体育在线:2018528日(星期一)上午09:30

  

报告地点:理学院二楼会议室

报告人:王浩副教授University of Alberta,2003年毕业于中国科学技术大学,获数学和计算机科学双理学学士学位,2006年于美国Arizona State University获博士学位; 20071月至7月为Arizona State University博士后; 20078月至20096月为Georgia Institute of Techonology博士后; 20097月至20156月任Unviersity of Alberta助理教授; 20157月至今在University of Alberta任终身副教授。公开发表SCI论文近50篇,主持加拿大自然科学和工程研究基金(NSERC)项目4项。

报告摘要: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 Schwarz symmetrization rearrangement arguments, 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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