活動時間：8:00

活動日期：2018-10-27

地點：長安校區 數學與信息科學學院學術交流廳

主辦單位：數學與信息科學學院

講座題目1：Existence and Convergence to a Propagating Terrace in Time-Periodic Reaction-Diffusion Equations

講座時間：8:00-8:40

報告人：王智誠 教授

講座內容簡介：

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 $t\to\infty$.

講座人簡介：

王智誠，蘭州大學數學與統計學院教授，博士生導師。1994年本科畢業于西北師范大學，2007年在蘭州大學獲理學博士學位，2008年3月至2009年3月在加拿大約克大學從事博士后工作一年，2014年到法國波爾多大學訪問。1994年7月開始在河西學院開始工作，2007年7月開始在蘭州大學工作。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等雜志發表SCI論文60多篇，其中多篇論文入選ESI高引用論文，一篇論文入選2008年“中國百篇最具影響國際學術論文”。 2011年獲得甘肅省自然科學二等獎，主持完成兩項國家自然科學基金面上項目以及教育部博士點基金（新教師類）等多項省部級項目，正在參加一項國家自然科學基金重點項目。目前擔任兩個SCI雜志International  J.  Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的編委。

 講座題目2：Recent Development on a Lotka-Volterra Competition Diffusion Advection System

講座時間：8:40-9:20

報告人：周鵬 教授

講座內容簡介：

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.

講座人簡介：

周鵬，上海師范大學數學系教授，上海市東方學者。2015年畢業于上海交通大學，獲理學博士，師從肖冬梅教授。2015年-2017年受大西洋數學科學研究聯盟（AARMS）資助，在加拿大紐芬蘭紀念大學從事博士后研究，合作導師為Xiao-Qiang Zhao教授。 目前，周鵬教授的主要研究興趣是偏微分方程和單調動力系統，其部分研究成果發表在J. Math. Pure Appl., J. Funt. Anal.,  Calc. Var. Partial Differential Equations, J. Differential Equations等學術期刊上。

 講座題目3：Boundedness, stabilization and pattern formation driven by density suppressed motility

講座時間：9:20-10:00

報告人：金海洋 教授

講座內容簡介：

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).

講座人簡介：

金海洋，華南理工大學副教授，2014年在香港理工大學獲得博士學位，主要從事非線性偏微分方程的研究，近5年在 JDE，Nonliearity, DCDS，SIAM J. Appl. Math. 等重要學術期刊上發表研究論文18篇，目前正主持國家自然科學面上項目基金、青年基金項目各一項。

 講座題目4：Propagation of monostable traveling fronts in discrete periodic media with delay

講座時間：10:10-10:50

報告人：吳事良 教授

講座內容簡介：

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.

講座人簡介：

吳事良，西安電子科技大學教授，博導。2003年6月本科畢業于蘭州大學數學系， 2006年6月畢業于蘭州大學獲應用數學專業理學碩士學位，2009年12月畢業于西安電子科技大學獲應用數學專業理學博士學位。2013至2014年于美國邁阿密大學數學系公派訪問。2014年破格晉升為教授。吳事良教授的研究方向動力系統、微分方程以及生物數學，有關研究成果總結發表在三十余篇學術論文中并發表在Trans AMS、J Differential Equations、J Dynam Diff Eqns、Discrete Cont Dyn Sys、Proc Royal Soc Edinburgh A等學術期刊。承擔和主持國家自然基金面上項目，青年基金與天元專項各一項，陜西省自然基金一項。獲2012年陜西省優秀博士論文，獲第十一屆陜西青年科技獎。

講座題目5：Global existence and asymptotic behavior for the three-dimensional non-conservative compressible two-fluid model in a bounded domain

講座時間：10:50-11:40

報告人：姚磊 教授

講座內容簡介：

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.

講座人簡介：

姚磊，西北大學教授，博士生導師，主要從事流體力學中的偏微分方程數學理論的研究。2010年在華中師范大學獲理學博士學位，曾獲全國百篇優秀博士學位論文獎、陜西省科學技術獎、陜西省青年科技新星。