双波作用模型在三次非线性介质中的整体解存在的最佳条件

对一类耦合非线性Schr(?)dinger方程组进行了讨论,该方程组模拟了双波在三次幂介质中的相互作用.通过构造一个交叉强制变分问题和所谓的发展流的不变流形,获得了其初值问题整体解存在的一个最佳条件.另外还证明了驻波的不稳定性.     

双波作用模型在三次非线性介质中的整体解存在的最佳条件

对一类耦合非线性Schr(o)dinger方程组进行了讨论,该方程组模拟了双波在三次幂介质中的相互作用.通过构造一个交叉强制变分问题和所谓的发展流的不变流形,获得了其初值问题整体解存在的一个最佳条件.另外还证明了驻波的不稳定性.     

第25卷B辑第4期(2004)目次和提要

非线性弹性动力学方程组在星形域外Dirichlet型初边值问题解的几乎整体存在性 辛杰 秦铁虎 该文讨论非线性弹性动力学方程组在星形域外的Dinchlet型初边值问题,对小初值证明了该问题解的几乎整体存在性,给出解的生存区间的下界.     

一类奇异拟线性椭圆型方程组的可解性

研究了一类P-Laplacian方程组边值问题正径向整体解的存在性和唯一性.首先,利用隐函数定理证明了该问题的局部解的存在性与唯一性,以及解对初值的连续依赖性.最后,证明了该问题存在唯一的正径向整体解.     

广义Davey-Stewartson方程组的整体解及自相似解

本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论.     

一类非线性抛物型方程组解的整体存在及爆破

研究了一类带有非线性边界条件的非线性抛物型方程组解的整体存在及解在有限时刻爆破问题.通过构造方程组的上、下解.得到了解整体存在及解在有限时刻爆破的充分条件.对指数型反应项和边界流采用了常微分方程方法构造其上下解,而其它例如第一特征值等方法运用于该方程就比较困难.     

黎曼曲面到S2的非均匀Landau-Lifshitz方程组

本文主要考虑从黎曼曲面到S2的非均匀Landau-Lifshitz方程组的解的存在性.证明了对于适当初始值,方程是存在唯一的,除有限个点外处处正则的整体解,并且该解在每一奇点处爆破成一个光滑的调和映射.还讨论了方程组在IR22上定常解的不存在性.     

一类具交错扩散的强耦合退化抛物方程组解的整体存在与非存在性

本文研究了一类具交错扩散的强耦合拟线性退化抛物方程组初边值问题正古典解的局部存在,整体存在与非整体存在性.利用正则化方法和先验估计技巧证明了该问题正古典解的局部存在性,并且分别给出了该问题是否存在整体古典解的充分条件.结果表明当种群内竞争强于种群间互惠作用时,此问题存在整体解;而当两种群具有强互惠作用时,所有解都是非整体的.     

边界耦合的非Newton渗流方程组解的临界曲线与非灭绝条件

利用上解与下解方法研究了多维空间RN中一类在边界耦合的非Newton渗流方程组,得到了方程组解的临界整体存在曲线与Fujita临界曲线.结果表明,方程组解的两种临界曲线不仅依赖于问题中的参数,而且还与空间的维数N有关,这与维数N=1时的已有结果有很大的区别.此外,还给出了该方程组解的非灭绝条件.     

具有某种源气体动力学方程组定解问题整体解的渐近性

对于方程组(1.1)的齐次形式(f(u)=0),Kazhikhov 证明了初边值问题(1.1)—(1.3)的解的整体存在性以及渐近性.随后,陈贵强、陆云光对于非齐次方程组(1.1)的初边值问题的解的整体存在性给予了证明.本文研究方程组(1.1)的初边值问题整体解的渐近性.     

一类具有饱和传染力的Schoner竞争系统的概周期解

对一类具有饱和传染力的Schoner竞争系统进行了研究,得到了系统持久生存和任一正解全局渐近稳定的充分条件;同时当系统是概周期系统时,通过构造适当的Liapunov函数,建立了相应系统存在唯一、全局渐近稳定的概周期正解的充分判据.     

Qualitative analysis of a coupled reaction-diffusion model in biology with time delays

Certain biochemical reaction can be modeled by a coupled system of time-delayed ordinary differential equations and linear parabolic partial differential equations. In a three-compartment model these equations are coupled through the boundary conditions. The aim of this paper is to give a qualitive analysis of this unusual coupled system. The analysis includes the existence and uniqueness of a global solution, explicit upper and lower bounds of the solution, and global stability of a steady-state solution. The global stability result is with respect to any nonnegative initial perturbation and is independent of the time delays in the process of reaction. Special attention is given to the Goodwin model for biochemical control of genes by a negative feedback mechanism with time delay and diffusion.     

Stabilization of stationary affine control systems with discrete time

We obtain new sufficient conditions for the local and global asymptotic stabilization of the zero solution of a nonlinear affine control system with discrete time and with constant coefficients by a continuous state feedback. We assume that the zero solution of the free system is Lyapunov stable. For systems with linear drift, we construct a bounded control in the problem of global asymptotic state and output stabilization. Corollaries for bilinear systems are obtained.     

On the global existence and small dissipation limit for generalized dissipative Zakharov system

This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.     

Dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate

In this paper, the dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate are analyzed. The existence and uniqueness of the global positive solution is proved by constructing the equivalent system without pulses. The threshold which determines the extinction and persistence of the disease is obtained. The global attraction of disease-free periodic solution is addressed. Sufficient condition for the existence of a positive periodic solution is established. These results are supported by computer simulations.     

Global attractors for porous-elasticity system from second spectrum viewpoint

This paper is concerned with the global attractors for a new partially damped porous-elasticity system by taking a truncated version which is free of blow-up on second wave speed. We establish the global well-posedness of the system via Faedo–Galerkin method. By considering only one damping term acting on the volume fraction in the system we prove the existence of absorbing set for the solution semigroup regardless any relationship between coefficients of the system. Finally, by using Lyapunov and recent quasi-stability methods we prove the existence of smooth global attractors with finite fractal dimension.     

Global nonexistence of positive initial energy solution for coupled quasilinear system

In this paper, we consider global nonexistence of a solution for coupled quasilinear system with damping and source under Dirichlet boundary condition. We obtain a global nonexistence result of solution by using the perturbed energy method, where the initial energy is assumed to be positive. Copyright © 2017 John Wiley & Sons, Ltd.     

一类Lotka-Volterra竞争生态系统的周期解

讨论一类特殊的n种群LotkaVolterra竞争生态系统的周期解,应用拓扑度理论中的延拓定理和Lyapunov泛函方法,得到了这类系统周期解的存在性和全局渐近稳定性的充分判据.     

基于GMCR-NPAWLAK混合模型的冲突分析研究

冲突分析图模型中,决策者的态度只有肯定和否定两种,实际问题中往往不止两种;新PAWLAK冲突模型(NPAWLAK模型)将冲突系统中决策者的三种态度扩展到决策争端的三种程度,符合实际情况,因而研究冲突系统中决策者的偏好排序和全局可行方案对决策者的策略选择具有重要意义。本文在NPAWLAK模型的基础上,引入冲突分析图模型理论(GMCR),提出GMCR-NPAWLAK冲突分析混合模型。该混合模型首先拓展和改进的策略优先排序法,实现了冲突系统中各决策者的客观偏好排序;同时,模型给出了全局可行方案的算法,该算法依据决策者的偏好排序分析结果找出系统的全局可行方案。最后,本文以某企业劳资关系的NPAWLAK冲突为例,对冲突系统进行建模和偏好分析,得到了冲突各方的偏好序列和全局可行方案,同时验证了混合模型的有效性。