報告題目：高維脈沖反應擴散對流模型
(On impulsive reaction-diffusion-advection models in higher dimensions)
報告時間：2018年5月28日（星期一）上午09:30
報告地點：必一体育平台二樓會議室
報告人：王浩副教授（University of Alberta）,2003年畢業於中國科學技術大學,獲數學和計算機科學雙理學學士學位，2006年於美國Arizona State University獲博士學位; 2007年1月至7月為Arizona State University博士後; 2007年8月至2009年6月為Georgia Institute of Techonology博士後; 2009年7月至2015年6月任Unviersity of Alberta助理教授; 2015年7月至今在University of Alberta任終身副教授。公開發表SCI論文近50篇，主持加拿大自然科學和工程研究基金（NSERC）項目4項。
報告摘要：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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