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

内容簡介：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.

報告人：哈爾濱工業大學  王明新  教授

報告人簡介：哈爾濱工業大學特聘教授和二級教授，博士生導師，國務院政府特殊津貼獲得者。曾任江蘇省數學會副理事長，東南大學理學院副院長、數學系主任、應用數學碩士和博士點學科負責人、二級教授和特聘教授, 江蘇省重點學科“應用數學”首席科學家。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. 等期刊發表被 SCI檢索的論文220餘篇。科學出版社出版和高等教育出版社專著6本，參與編寫了科學出版社出版的“數學大辭典”，清華大學出版社出版教材4本。主持完成國家自然科學基金項目9項，在研1項；主持完成省部級項目9項。獲得教育部科技進步三等獎2次，江蘇省科技進步二等獎1次，高等學校科學研究優秀成果獎自然科學二等獎1次，江蘇省首屆青年科學家獎提名獎，河南省青年科技獎，江蘇省優秀研究生指導教師，華英文化教育基金獎。

時  間：2019年4月18日（周四）下午4：00始

地  點：南海樓224室

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2019年4月18日