报告题目：The selection mechanism of asymptotical speeds of spread to monostable semiflows

报 告 人：马满军 教授 浙江理工大学

照片：

邀请人：吴事良

报告时间：2020年8月25日（周二） 15：00-16：00

腾讯会议ID：311 110 922 密码：123456

报告人简介：马满军，浙江理工大学教授。多次应邀访问美国圣地亚哥州立大学、加拿大纪念大学、香港理工大学，进行合作研究。主要从事微分方程存在性与稳定性理论及动力系统非线性波理论的研究，并且利用相关理论研究Bose-Einstein凝聚体中孤立子、生物生态学、化学等背景学科领域数学模型的动力学性质。以第一作者在SIAM Journal on Mathematical Analysis、Journal of Differential Equations、SIAM Journal on Applied Mathematics、Nonlinearity、Proceedings of the Royal Society A 、Discrete and Continuous Dynamical Systems及Physical Review A等国内外重要学术刊物发表论文30余篇；主持研究国家自然科学基金面上项目、国家教育部留学归国人员科研启动基金各一项；参与研究国家科技部973项目重大基础研究前期研究专项一项。

报告摘要： This talk is about an abstract monotone semiflow which has exactly two fixed points. A necessary and sufficient condition for the nonlinear selection of the spreading speed is established. Based on this result, we then derive conditions under which the linear or nonlinear selection is realized by way of comparison principle. Our results on nonlinear selection can be viewed as breakthroughs in this topic; and for the linear selection, we successfully improve previous conventional results that always require the monotone semiflow is dominated by its linear map. The applications to various biological models are also successful. We establish a series of new results to reaction-diffusion models with delay interactions, a lattice system, a scalar integro-difference equation and a cooperative system, which completely solve some open problems and conjectures in the related references.