题  目：Spatial spreading of a logistic SI epidemic model with degenerate diffusion and double free boundaries

内容简介：This talk concerns with a logistic SI epidemic model with degenerate diffusion and double free boundaries to describe the spatial spreading of disease. The existence, uniqueness and estimates of the global solution are discussed firstly. Then we prove a spreading-vanishing dichotomy, namely the infective class either successfully spreads to infinity, or it spreads within a bounded area and vanish eventually, while the sensitive class stabilizes at a positive equilibrium state. Besides, the long time behavior of solution and criteria for spreading and vanishing are also obtained. The upper and lower solutions method helps us to overcome some difficulties brought by the degenerate diffusion and non-monotonicity of the model. Especially, we find the Basic Reproduction Number R which measures the spreading and vanishing: when R<1,  vanishing always happens and the disease will die out; when R>1, whether or not to vanish depends on the size of the initial habitat and the rate of expansion. This phenomenon reveals the role of free boundaries in the epidemic.

报告人：哈尔滨工业大学  王明新  教授

报告人简介：哈尔滨工业大学特聘教授和二级教授，博士生导师，国务院政府特殊津贴获得者。曾任江苏省数学会副理事长，东南大学理学院副院长、数学系主任、应用数学硕士和博士点学科负责人、二级教授和特聘教授, 江苏省重点学科“应用数学”首席科学家。在Proc. London Math. Soc., Trans. Amer. Math. Soc., Indiana Univ. Math. J., J. Math. Pures Appl., J. Func. Analysis, SIAM J. Math. Anal., SIAM J. Appl. Math., J. Diff. Equns., J. London Math. Soc., Physica D, J. Dyn. Diff. Equat. 等期刊发表被 SCI检索的论文220余篇。科学出版社出版和高等教育出版社专著6本，参与编写了科学出版社出版的“数学大辞典”，清华大学出版社出版教材4本。主持完成国家自然科学基金项目9项，在研1项；主持完成省部级项目9项。获得教育部科技进步三等奖2次，江苏省科技进步二等奖1次，高等学校科学研究优秀成果奖自然科学二等奖1次，江苏省首届青年科学家奖提名奖，河南省青年科技奖，江苏省优秀研究生指导教师，华英文化教育基金奖。

时  间：2019年4月18日（周四）下午4：00始

地  点：南海楼224室

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信息科学技术学院

2019年4月18日