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数学与信息科学学院系列学术报告

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讲座题目:数学与信息科学学院系列学术报告
讲座人: 王智诚 教授等
讲座时间:8:00
讲座日期:2018-10-27
地点:长安校区 数学与信息科学学院学术交流厅

讲座题目1:Existence and Convergence to a Propagating Terrace in Time-Periodic Reaction-Diffusion Equations
讲座时间:8:00-8:40
报告人:王智诚 教授
讲座内容简介:
This talk is concerned with the long time behavior of the solution of a time periodic reaction-diffusion equation
\begin{equation}
u_{t}(x,t)=u_{xx}(x,t)+f(t,u(x,t)),  \forall x\in\mathbb{R},\,t>0  
\end{equation}
with the Heaviside type initial value, where $f(t,u)$ is $T$-periodic in time variable $t$. Under some suitable conditions on $f$, we first show some properties of the $\omega$-limit set by the zero-number argument. Then we show that the solution around a given level set converges to a pulsating traveling front connecting two of periodic solutions. Finally, we show the existence of a minimal propagating terrace in some specific sense by an induction argument. Moreover, we can show that the solution converges to such a minimal propagating terrace as $t\to\infty$.
讲座人简介:
王智诚,兰州大学数学与统计学院教授,博士生导师。1994年本科毕业于西北师范大学,2007年在兰州大学获理学博士学位,2008年3月至2009年3月在加拿大约克大学从事博士后工作一年,2014年到法国波尔多大学访问。1994年7月开始在河西学院开始工作,2007年7月开始在兰州大学工作。在Trans. AMS、SIAM J. Math. Anal.、JMPA、Calc. Var. PDE、JDE、JDDE、Nonlinearity、J. Math. Biol.、J. Nonlinear Sci、Proc. Royal. Soc. A、Proc. Royal. Soc. Edinburgh A、DCDS等杂志发表SCI论文60多篇,其中多篇论文入选ESI高引用论文,一篇论文入选2008年“中国百篇最具影响国际学术论文”。2011年获得甘肃省自然科学二等奖,主持完成两项国家自然科学基金面上项目以及教育部博士点基金(新教师类)等多项省部级项目,正在参加一项国家自然科学基金重点项目。目前担任两个SCI杂志International  J.  Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的编委。


讲座题目2:Recent Development on a Lotka-Volterra Competition Diffusion Advection System
讲座时间:8:40-9:20
报告人:周鹏 教授
讲座内容简介:
In this talk, we will mainly talk about the dynamics of a classical Lotka-Volterra competition-diffusion-advection system arising in river ecology. Different to the traditional diffusive case, now the linearized operator is non-self-adjoint, which gives arise new difficulty to study properties of both semi-trivial and co-existence steady states. We develop some analytic approach to overcome the emerging difficulties.
讲座人简介:
周鹏,上海师范大学数学系教授,上海市东方学者。2015年毕业于上海交通大学,获理学博士,师从肖冬梅教授。2015年-2017年受大西洋数学科学研究联盟(AARMS)资助,在加拿大纽芬兰纪念大学从事博士后研究,合作导师为Xiao-Qiang Zhao教授。目前,周鹏教授的主要研究兴趣是偏微分方程和单调动力系统,其部分研究成果发表在J. Math. Pure Appl., J. Funt. Anal.,  Calc. Var. Partial Differential Equations, J. Differential Equations等学术期刊上。

讲座题目3:Boundedness, stabilization and pattern formation driven by density suppressed motility
讲座时间:9:20-10:00
报告人:金海洋 教授
讲座内容简介:
In this talk, we are concerned with a  reaction-diffusion system with density suppressed motility in a two dimensional  bounded domain with homogeneous Neumann boundary conditions. By employing the weight energy estimates, we establish the existence of global  classical solution with uniform-in-time bound. Furthermore, the large time behavior of solution is studied by constructing some Lyapunov functional for large value of the intrinsic growth rate of cell. At last,  if the value of the intrinsic growth rate of cell is small,  we perform the linear stability analysis and numerically illustrate various patterns (like aggregation and wavefronts) formed by the model. Our simulations show that the cell growth plays an indispensable role in generating wave propagation. This is a joint work with Prof. Yong-Jung Kim (KAIST) and Prof. Zhi-An Wang (Polyu).
讲座人简介:
金海洋,华南理工大学副教授,2014年在香港理工大学获得博士学位,主要从事非线性偏微分方程的研究,近5年在JDE,Nonliearity, DCDS,SIAM J. Appl. Math. 等重要学术期刊上发表研究论文18篇,目前正主持国家自然科学面上项目基金、青年基金项目各一项。

讲座题目4:Propagation of monostable traveling fronts in discrete periodic media with delay
讲座时间:10:10-10:50
报告人:吴事良 教授
讲座内容简介:
In this talk, we study the front propagation for a class of discrete periodic monostable equations with delay and nonlocal interaction. We first establish the existence of rightward and leftward spreading speeds and prove their coincidence with the minimal wave speeds of the pulsating traveling fronts in the right and left directions, respectively. The dependency of the speeds of propagation on the heterogeneity of the medium and the delay term is also investigated. We find that the periodicity of the medium increases the invasion speed, in comparison with a homogeneous medium; while the delay decreases the invasion speed. Further, we prove the uniqueness of all noncritical pulsating traveling fronts. Finally, we show that all noncritical pulsating traveling fronts are globally exponentially stable, as long as the initial perturbations  around them are uniformly bounded in a weight space.
讲座人简介:
吴事良,西安电子科技大学教授,博导。2003年6月本科毕业于兰州大学数学系, 2006年6月毕业于兰州大学获应用数学专业理学硕士学位,2009年12月毕业于西安电子科技大学获应用数学专业理学博士学位。2013至2014年于美国迈阿密大学数学系公派访问。2014年破格晋升为教授。吴事良教授的研究方向动力系统、微分方程以及生物数学,有关研究成果总结发表在三十余篇学术论文中并发表在Trans AMS、J Differential Equations、J Dynam Diff Eqns、Discrete Cont Dyn Sys、Proc Royal Soc Edinburgh A等学术期刊。承担和主持国家自然基金面上项目,青年基金与天元专项各一项,陕西省自然基金一项。获2012年陕西省优秀博士论文,获第十一届陕西青年科技奖。

讲座题目5:Global existence and asymptotic behavior for the three-dimensional non-conservative compressible two-fluid model in a bounded domain
讲座时间:10:50-11:40
报告人:姚磊 教授
讲座内容简介:
In this talk, we consider the initial boundary value problem to a non-conservative compressible two-fluid model with unequal pressure functions P^+ \neq P^- in bounded domains of \mathbb{R}^3 with slip boundary. Firstly, we establish a series of energy estimates, among which the isothermal coordinates transformations in local regions is used to get the higher-order estimates near the boundary. The existence of global classical solution is obtained, provided that the initial perturbations is small in H^3-norm. Furthermore, the asymptotic behavior of the solutions is also deduced.
讲座人简介:
姚磊,西北大学教授,博士生导师,主要从事流体力学中的偏微分方程数学理论的研究。2010年在华中师范大学获理学博士学位,曾获全国百篇优秀博士学位论文奖、陕西省科学技术奖、陕西省青年科技新星。

 

 

 
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