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第22期学术报告:Domain decomposition methods for a class of spatially heterogeneous delayed reaction–diffusion equations

时间:2019-06-06 09:07:05  作者:  点击: 107 次

22期学术报告

题 目Domain decomposition methods for a class of spatially heterogeneous delayed reaction–diffusion equations

时  间:2019年6月7日下午1630-17:30

地  点8号楼425

报告人易泰山

   简介1999 年和2004 年分别获湖南大学应用数学学士学位和博士学位。2006年9月至2008年8月先后在加拿大西安大略大学(Western Ontario University)、劳瑞尔大学(Wilfrid Laurier University)及约克大学(York University)做博士后。2005起先后在湖南大学、中南大学、中山大学任教,现为中山大学数学学院(珠海)教授、博士生导师。主要从事泛函微分方程、反应扩散方程、动力系统及其应用方面的研究,已在 SIAM Journal on Mathematical Analysis, Journal of Differential Equations, Proc. R. Soc. Lond. Ser. A、J. Dynam. Differential Equations 等国际著名刊物发表论文三十余篇。主持了3 项国家自然科学基金项目和1项湖南省杰出青年基金,2008年入选教育部新世纪优秀人才支持计划

讲座摘要We derive and study a class of delayed reaction–diffusion equations with spatial heterogeneity, which models the population of a single species with different habitats for mature and immature individuals. We introduce new solid cones, obtain spectral bounds of several spatial heterogeneous operators, and establish limiting non-negativeness property for the whole space and the eventual comparison principle for bounded domains. As a result, we develop new domain decomposition methods so that one can compare solutions with those to associated equations from a suitable bounded spatial domain to the whole space. Then by employing domain decomposition methods and dynamical system approaches, we obtain threshold results under the supremum norm. These results are greatly different from the existing ones of other evolution equations in unbounded domains or the whole space. The main results are applied to two examples with the Ricker birth function and with the Mackey–Glass birth function. It reveals that the size of the immature habitat can affect the reproduction and spread of the population.

 

 

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