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题目：Stability Analysis for Imcompressible Navier-Stokes Equations with Navier Boundary Conditions报告人：丁时进 教授（华南师范大学探花视频 ）地点：宁静楼108室时间：2017年11月15日（周三） 下午16：00-17:00欢迎广大师生参加

We develop the Lawson-Osserman's works on minimal graphs. Firstly, we construct a constellation of uncountably many Lawson-Osserman spheres, which are minimal in Euclidean spheres and therefore generate Lawson-Osserman cones that correspond to Lipschitz but non-differentiable solutions to the minimal surface system. Then, by the theory of autonomous systems in plane, we find for each Lawson-Osserman cone an entire minimal graph having it as tangent cone at infinity.

In this talk, we shall discuss the global stability of prey-taxis model with a variety of predator-prey interactions. In the previous limited results, various assumptions are imposed to ensure the boundedness of classical solutions. In our work, we shall first remove those conditions, and then establish the asymptotic behavior of solutions and identify the conditions under which the predator-prey asymptotic outcomes including coexistence, exclusion and extinctions will be achieved. Applications of our results will be discussed and some open questions will be discussed.

This talk is concerned with the optimal harvesting of a predator–prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin’s maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results.

An epidemic model for yellow fever virus is formulated and used to study the 2016 yellow fever (YF) outbreak in Luanda, Angola. We explore the complex vector-host dynamics of this system taking into account mosquito abundance, vaccination and asymptomatic cases in the human population, that are generally not included in other modelling studies of YF. The model successfully fits existing time-series of weekly reported cases and deaths from YF during the epidemic. This allows us to study the impact of the vaccination campaign in Luanda and hypothetical delayed vaccination scenarios.

The Lyapunov functionals are very useful for the analysis of the global asymptotic behavior of the delay differential equations models. In this talk, we present several delay epidemiological models, in which time delays appear in different position of models and describe different biological meanings. Several Lyapunov functionals were applied to delay models above. And we develop further the Lyapunov functional to more delay differential equations in population dynamics.

Diapause (or named as dormancy traditionally) as a process of physiological rest is widespread in insects and other invertebrate organisms, which serves as a key survival mechanism in response to adverse environmental conditions. In this paper, a novel modelling framework is proposed to investigate the effects of diapause on population growth, where diapause period is taken as an independent dynamic process, during which the population dynamics is completely different from that in the normal developmental and post-diapause periods. To explicitly describe population growth with different diapausing stages, either immature or adult ones, two different delay differential equation models are constructed with an emphasis on mosquitoes.

In this talk, we will prove the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality. Moreover, the equivalence between the dual log-Brunn-Minkowski inequality and the dual log-Minkowski inequality is demonstrated.