数学与系统科学学院学术报告

时间：2019年11月19日（周二）09：00-11：00

地点：工业中心506室

报告一

报告题目：Period function of Hamiltonian systems with separable variables

报告人简介: 张祥，上海交通大学特聘教授（享受国务院特殊津贴，二级教授、博导），欧洲科学与艺术院院士。主要从事动力系统的定性、分支和可积理论的研究。所得结果部分发表在《American J. Math. Transactions of Amer. Math. Soc.》, 《Communications Math. Phys.》, 《J. Functional Analysis》, 《J. Nonlinear Sciences》 和《 J. Differential Equations》等国际一流数学杂志上。多次应邀在欧美举行的动力系统国际会议上做大会特邀报告。目前担任中国数学会奇异摄动专业委员会主任，中国数学会理事，以及国际SCI杂志《Qualitative Theory of Dynamical Systems》和《International J. Bifurcation and Chaos》的Associate编委等。

 内容摘要：In this talk we intrudoce our recent results on the period function of  planar Hamiltonian differential systems with separable variables. The results are on sufficient conditions for monotonicity of the period  function and uniqueness of critical periods, and also on the limit of the  period function near the  boundary of the period annulus of the center. 

报告二

报告题目：Wolbachia infection model with free boundary

报告人简介: 郭志明，广州大学数学与信息科学学院教授、博士生导师，第十一届广东省人大代表。2001年博士毕业于中山大学。多年来一直从事离散系统、泛函微分方程及生物数学模型的理论与应用研究，在《Journal of Differential Equations》、《Journal of London Mathematical Society》、《Journal Dynamics and Differential Equations》、《Journal of Mathematical Biology》、《中国科学》等国际国内重要刊物上发表论文60多篇，其中SCI收录50多篇。先后主持国家自然科学基金3项、参加国家自然科学基金重点项目1项。
内容摘要：Scientists have been seeking ways for many years to use Wolbachia to eliminate the mosquitoes that spread human diseases. Could Wolbachia be the determining factor in controlling the mosquito-borne infectious diseases?  To answer this question mathematically, we develop a reaction-diffusion model with free boundary in one-dimensional environment. We divide the female mosquito population into two groups: one is the uninfected mosquito population that grows in the whole region while the other is the mosquito population infected with Wolbachia that occupies a finite small region and invades the environment with a spreading front governed by a free boundary satisfying the well-known one-phase Stefan condition. For the resulting free boundary problem, we establish criteria for spreading and vanishing. Our results provide useful insights on designing feasible mosquito releasing strategy to invade the whole female mosquito population with Wolbachia infection and thus eventually eradicate the mosquito-borne diseases.          

    欢迎老师、同学们参加！

                             数学与系统科学学院

                             2019年11月12日