Minkowski problem is one of a central problem in convex geometry. In this talk, we will present our recent work on Lp Minkowski problem for capacity.

Consider weak solutions of the instationary Navier-Stokes system in a three-dimensional bounded smooth domain $/Omega$. It is well known that any solenoidal initial value $u_0$ in $L^2(/Omega)$ with a vanishing normal component on the boundary admits a global in time weak solution. Moreover, if $u_0 /in H^1$ or even only $u_0 /in /mathcal{D}(A^{1/4})/subset L^3$, where $A =-P/Delta$ denotes the Stokes operator, then $u_0$ admits a unique local in time regular (strong) solution in Serrin’s class $L^s(0,T;L^q (/Omega))$ where $2/s + 3/q = 1$ for some $T = T(u_0)/leq/infty$.

题目：Stability Analysis for Imcompressible Navier-Stokes Equations with Navier Boundary Conditions报告人：丁时进 教授（华南师范大学太平洋在线会员登录）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.