“2016年动力系统及应用研讨会”
会 议 日 程
时间：2016年3月13日 地 点：国际会议中心3楼第二会议室
| 时间 |
报告人 |
报告题目 |
| 8:15-8:30 |
开幕式（卢玉峰）, 合影留念 |
| 主持人：李勇 |
| 8:30-9:00 |
韩月才 吉林大学 |
Stochastic maximum principle for controlled systems driven by fractional motions |
| 9:00-9:30 |
衣凤岐 哈尔滨工程大学 |
Spatiotemporal patterns of a reaction-diffusion substrate-inhibition Seelig model |
| 9:30-10:00 |
季春燕 常熟理工学院 |
Threshold behaviour of a stochastic SIR model |
| 10:00-10:20 |
休息 |
| 主持人：韩月才 |
| 10:20-10:50 |
李春 南京大学 |
Weak multi-symplectic reformulation and geometric integration for the nonlinear and delta-potential Schrödinger equations |
| 10:50-11:20 |
张静静 河南理工大学 |
New energy-preserving schemes for Klein-Gordon-Schrödinger equations |
| 11:20-11:50 |
王旭 中国科学院 |
Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme |
| 午餐与休息 |
| 主持人：洪佳林 |
| 14:00-14:30 |
冀书关 |
Effect of (small) permanent charge and channel geometry on ionic flows via classical Poisson-Nernst-Planck models |
| 14:30-15:00 |
许璐 吉林大学 |
Lower dimensional tori for multi-scale, nearly integrable Hamiltonian systems |
| 15:00-15:30 |
高鹏 东北师范大学 |
Null controllability of forward stochastic Kuramoto-Sivashinsky equations and backward linear stochastic Kuramoto-Sivashinsky equations |
| 15:30-15:50 |
休息 |
| 主持人：冀书关 |
| 15:50-16:20 |
李晓月 东北师范大学 |
Switching diffusion logistic models involving singularly perturbed Markov chains: weak convergence and stochastic permanence |
| 16:20-16:50 |
魏元鸿 吉林大学 |
Existence of solutions for a system of diffusion equations with spectrum point zero |
| 16:50-17:20 |
刘智慧 中国科学院 |
Approximation of stochastic evolution equations driven by additive fractional noises |
| 18:00 晚餐 |
时间：2016年3月14日 地 点：国际会议中心3楼第二会议室
| 时间 |
报告人 |
报告题目 |
| 主持人：孔令华 |
| 8:30-9:00 |
从福仲 空军航空大学 |
Quasi effective stability of Hamilton systems |
| 9:00-9:30 |
梁树青 吉林大学 |
The multiplicity and stability of T-periodic solutions for a class of second order differential equation |
| 9:30-10:00 |
陈锋 东北师范大学 |
Almost automorphic solutions for stochastic differential equations driven by fractional Brownian motion |
| 10:00-10:20 |
休息 |
| 主持人：从福仲 |
| 10:20-10:50 |
孔令华 江西师范大学 |
High resolution numerical method for the multidimensional convection-diffusion equations |
| 10:50-11:20 |
苗利军 中国科学院 |
Hölder Continuity for parabolic Anderson equation with non-Guassian noise |
| 11:20-11:50 |
周炜恩 中国科学院 |
Projection methods for stochastic differential equations with conserved quantities |
| 12:00午餐 |
| 下午：自由讨论 |
| 18:00晚餐 |
Abstracts of Workshop Talks
Almost automorphic solutions for stochastic differential equations driven by fractional Brownian motion
Feng Chen
chenf101@nenu.edu.cn
Northeast Normal University
Abstract: This paper concerns a class of stochastic differential equations driven by fractional Brownian motion. The existence and uniqueness of almost automorphic solutions in distribution are established provided the coefficients satisfy some suitable conditions. To illustrate the results obtained in the paper, a stochastic heat equation driven by fractional Brownian motion is considered.
Quasi effective stability of Hamilton systems
Fuzhong Cong
congfz67@126.com
Aviation University Air Force
Abstract: TBA
Null controllability of forward stochastic Kuramoto–Sivashinsky equations and backward linear stochastic Kuramoto–Sivashinsky equations
Peng Gao
gaopengjilindaxue@126.com
Northeast Normal University
Abstract: In this talk, we discuss the null controllability of forward stochastic linear Kuramoto–Sivashinsky (KS) equations and backward stochastic linear KS equations. The key point is to establish the Carleman estimates for stochastic fourth order forward parabolic equations and stochastic fourth order backward parabolic equations.
Stochastic maximum principle for controlled systems driven by fractional motions
Yuecai Han
hanyc@jlu.edu.cn
Jilin University
Abstract: We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst index H>1/2). We introduce a type of backward stochastic differential equations driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions to specify the necessary condition that the optimal control must satisfy. Our approach is to use conditioning and Malliavin calculus.
Threshold behaviour of a stochastic SIR model
Chunyan Ji
chunyanji80@hotmail.com
Changshu Institute of Technology
Abstract: In this paper, we investigate the threshold behavior of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.
Effect of (small) permanent charge and channel geometry on ionic flows via classical Poisson-Nernst-Planck models
Shuguan Ji
Abstract: TBA
High resolution numerical method for the multidimensional
convection-diffusion equations
Linghua Kong
konglh@mail.ustc.edu.cn
Jiangxi Normal University
Abstract: A class of high-order compact method has been studied which combines local one-dimensional strategy in time to numerically solve multidimensional convection-diffusion equations. The method is widely accepted due to it compactness, high accuracy. In this method the spatial derivatives are approximated implicitly rather than explicitly to improve the accuracy with smaller stencil. The local one-dimensional strategy is adopted in time to decrease the scale of the algebraic equations rendered by the numerical method. By Von Neumann approach, we can find that the proposed schemes are unconditionally stable. Some numerical results are reported to illustrate that the schemes are robust, efficient and accurate.
Weak multi-symplectic reformulation and geometric integration for the nonlinear and delta-potential Schrödinger equations
Chun Li
lichun@nju.edu.cn
Nanjing University
Abstract: In this report, we focus on an important model in condensed matter physics, i.e. the nonlinear Schrödinger equation (NLSE) with an inclusion of delta potentials. Due to the inclusion, the model can NOT be reformulated as a multi-symplectic Hamiltonian system as the normal NLSE. We thus propose a weak multi-symplectic reformulation for the model. Based on the reformulation, some geometric numerical methods are elaborately investigated. Numerical experiments are presented to validate our methods. Moreover, our discussion given here can be extended to general multi-symplectic Hamiltonian PDEs with finite inclusions of delta potentials.
Switching diffusion logistic models involving singularly perturbed Markov chains: weak convergence and stochastic permanence
Xiaoyue Li
lixy209@nenu.edu.cn
Northeast Normal University
Abstract: Focusing on stochastic dynamics involve continuous states as well as discrete events, this paper investigates stochastic logistic model with regime switching modulated by a singular Markov chain involving a small parameter. This Markov chain undergoes weak and strong interactions, where the small parameter is used to reflect rapid rate of regime switching among each state class. Two-time-scale formulation is used to reduce the complexity. We obtain weak convergence of the underlying system so that the limit has much simpler structure. Then we utilize the structure of limit system as a bridge, to invest stochastic permanence of original system driving by a singular Markov chain with a large number of states. Sufficient conditions for stochastic permanence are obtained. A couple of examples and numerical simulations are given to illustrate our results.
The multiplicity and stability of T-periodic solutions for a class of second order differential equation
Shuqing Liang
liangshuqing@jlu.edu.cn
Jilin University
Abstract: The problem of $T$-periodic solutions of second order differential equation is familiar to us. We show a general class of nonlinearity for the exact multiplicity and stability of $T$-periodic solutions of a class of second order differential equation. The proof is based on connections between degree theory and local index of periodic solutions, and Hill's equation.
Approximation of stochastic evolution equations driven by additive
fractional noises
Zhihui Liu
liuzhihui@lsec.cc.ac.cn
Chinese Academy of Sciences
Abstract: We analyze Galerkin schemes for stochastic evolution equations (SEEs) driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to 1/2 . We first regularize the noise by Wong-Zakai approximations and obtain its optimal order of convergence. Then we apply the Galerkin-type schemes to discretize the regularized SEEs. We find that the Wong-Zakai approximations simplify the error estimates of Galerkin schemes for SEEs, and our error estimates remove the infinitesimal factor ϵ appearing in various numerical methods for SEEs in the existing literatures.
Hölder continuity for parabolic Anderson equation with non-Guassian noise
Lijun Miao
miaolijun@lsec.cc.ac.cn
Chinese Academy of Sciences
Abstract: The global well-posedness of the parabolic Anderson equation driven by a non-Gaussian noise is presented. We also derive the spatial and temporal Hölder continuity of the mild solution based on its uniform boundedness.
Approximation of invariant measure for damped stochastic nonlinear Schrödinger equation via an ergodic numerical scheme
Xu Wang
wangxu@lsec.cc.ac.cn
Chinese Academy of Sciences
Abstract: We study the approximation of invariant measure for an ergodic damped stochastic nonlinear Schrödinger equation (NLSE) with additive noise. A spatial semi-discrete scheme and a fully discrete scheme for the damped stochastic NLSE are proposed. The ergodicity of the numerical solutions of both spatial semi-discretization and full discretization are proved. Also, we show that the approximation errors of invariant measure are $N^{-1}$ in spatial direction and $\tau^{1/2}$ in temporal direction.
Existence of solutions for a system of diffusion equations with spectrum point zero
Yuanhong Wei
yhwei@amss.ac.cn
Jilin University
Abstract: We consider the existence and multiplicity of homoclinic type solutions to a system of diffusion equations with spectrum point zero. By using some recent critical point theorems for strongly indefinite problems, we obtain at least one nontrivial solution and also infinitely many solutions.
Lower dimensional tori for multi-scale, nearly integrable Hamiltonian systems
Lu Xu
xulu@jlu.edu.cn
Jilin University
Abstract: In this presentation, we introduce a multi-scale nearly integrable Hamiltonian systems which naturally arise in planar and spatial lunar problems of celestial mechanics. It has been proved, under certain non-degenerate condition, most of the non-resonant, non-degenerate quasi-periodic invariant tori persist under sufficiently small perturbation. It motivates us to consider the persistence of lower dimensional tori on certain resonant surface. My presentation includes three parts, we first introduce the background of multi-scale systems, then we show our results for certain case, the last part is an example.
Spatiotemporal patterns of a reaction-diffusion substrate-inhibition Seelig model
Fengqi Yi
fengqi.yi@aliyun.com
Harbin Engineering University
Abstract: In this paper, the spatiotemporal patterns of a reaction-diffusion substrate-inhibition chemical Seelig model are considered. We first prove that this parabolic Seelig model has an invariant rectangle in the phase plane which attracts all the solutions of the model regardless of the initial values. Then, we consider the long time behaviors of the solutions in the invariant rectangle. In particular, we prove that, under suitable "lumped parameter assumption" conditions, these solutions either converge exponentially to the unique positive constant steady states or to the stable spatially homogeneous periodic solutions. Finally, we study the existence and non-existence of Turing patterns. To find parameter ranges where system does not exhibit Turing patterns, we use the properties of non-constant steady states, including obtaining several useful estimates. To seek the parameter ranges where system possesses Turing patterns, we use the techniques of global bifurcation theory. These two different parameter ranges are distinguished in a delicate bifurcation diagram. Moreover, numerical experiments are also presented to support and strengthen our analytical analysis. This is a joint work with Y. Liu and N. Tuncer.
New energy-preserving schemes for Klein-Gordon-Schrödinger equations
Jingjing Zhang
zhangjj@lsec.cc.ac.cn
Henan Polytechnic University
Abstract: In this talk, we focus on new conservative numerical methods for Klein-Gordon-Schrödinger equations. By expressing Klein-Gordon-Schrödinger equations in an infinite-dimensional Hamiltonian form, we firstly discretize spatial derivatives by using Sinc collocation method then approximate the associated semi-discrete ordinary differential equations by discrete gradient method. Based on two different discrete gradients, two new energy-preserving schemes are provided, respectively. Furthermore, it is proved that both schemes preserve the discrete charge conservation law as well. Finally, numerical experiments are presented to show the excellent long-time conservation behavior and efficiency of the new energy-preserving schemes.
Projection methods for stochastic differential equations with conserved quantities
Weien Zhou
weienzhou@outlook.com
Chinese Academy of Sciences
Abstract: In this talk, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The mean-square convergence orders of these methods under certain conditions are given, which can reach order 1.5 or even 2 according to the supporting methods embedded in the projection step. Finally, three numerical experiments are taken into account to show the superiority of the projection methods.
