Hodgkin-Huxley系统的渐进稳定性

用无穷维动力系统的方法研究了Hodgkin-Huxley神经脉冲传导系统的长时间行为.在齐次边界条件与非齐次边界条件证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而证明了该系统的渐进稳定性.     

Nehari流形在一个拟线性方程组中的应用

主要研究带有非齐次边界条件的拟线性椭圆方程组的正解问题,在合适参数条件下,用变分方法和流形方法得到该椭圆方程组正解的存在性和多解性.结论推广了近期发表的结果.     

具有扩散的Brusselator系统的Hopf分支

在齐次Neumann边界条件下,研究了Brusselator系统的Hopf分支问题.证明了当参数满足一定条件时,Brusselator常微分系统的平衡解和周期解是渐近稳定的,而相应的偏微分系统的空间齐次平衡解是不稳定的;如果适当选取参数,那么Brusselator偏微分系统出现Hopf分支.同时,利用中心流形定理证明了Hopf分支解的稳定性.最后给出一些数值模拟的例子以验证和补充理论分析结果.     

带位势的p-调和热流

在本文中我们考察从黎曼流形M到具左不变度量的齐次空间N的带位势的 p-调和映射热流,证明存在全局弱解.     

具有扩散的广义Brusselator系统的Hopf分歧

在齐次Neumann边界条件下,考虑广义Brusselator系统．首先讨论常微分系统Hopf分歧的存在性,得到渐近稳定的周期解．其次讨论具有扩散的偏微分系统,在扩散系数满足一定的条件下,得到超临界的Hopf分歧,并利用规范形理论和中心流形定理给出空间齐次周期解的渐近稳定性．最后,借助Matlab软件进行数值模拟,证明了定理的结论．同时,正平衡态解和空间非齐次周期解的描绘补充了理论分析结果．     

扰动非线性Schr(o)dinger方程组的动力性态

研究具周期边界条件的扰动非线性Schrodinger方程组的动力性态,首先,在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析,然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性.     

靶流形为齐次流形的弱次椭圆Q调和映射的正则性

该文证明了靶流形为齐次流形的弱次椭圆Q调和映射是内部正则的，这里Q是定义域的 齐次维数。这一结果推广了Hajlasz和Strzelecki的相应结果[2].作为推论得到了靶流形为齐次流形的p维p调和映射的正则性.     

扰动非线性Schrdinger方程组的动力性态

研究具周期边界条件的扰动非线性Schr dinger方程组的动力性态,首先,在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析,然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性·     

具有密度依赖的Monod-Haldane反应项捕食模型的动态分歧和跃迁

本文研究具有密度依赖的Monod-Haldane反应项捕食模型在齐次Dirichlet边界条件下的动态分歧和跃迁. 利用中心流形约化以及动态分歧理论, 在两种不同情形下分别得到跃迁类型及其判据, 给出吸引域的刻画, 补充和完善相关文献中的已有结果. 最后通过数值模拟验证理论分析的正确性并给出生物学解释.     

扰动非线性Schroedinger方程组的动力性态

研究具周期边界条件的扰动非线性Schroedinger方程组的动力性态，首先，在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析，然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性．     

瞬态波的高精度开路边条件*

文献[2～4]提出了一种用于瞬态波的自适应开路边条件(AOBC).克服了已有的开路边条件(OBC)应用范围狭窄的困难,可以适用于来波入射角在任意范围内变化的情况。本文则是以其中的一阶AOBC为基础,构造了一类新的高阶AOBC.并证明在所有同阶OBC中,只有这类AOBC才具有最高阶精度,而所有其之同阶的OBC的精度都要比它低。     

Global stability for n-species lotka-volterra systems with delay,ii: reducible cases,sufficiency

In this paper an n-species delayed Lotka-Volterra system without de1ayed intraspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays T_ij≥0 provided the interaction matrix A of the system satisfies the weakly diagonally dominant Condition (WDD)     

边界元凝聚解法解的存在唯一性条件

本文讨论了周边界元法分析三维弹性有摩擦接触问题形成的方程组。并对方程组进行凝聚，证明了凝聚后方程组解的存在唯一性的充分必要条件。     

On the imbedding problem for local fields

The imbedding problem of local fields is considered for the case where the whole of the group is a p-group having as many generators as the Galois group of the extension and the extension consists of a primitive root of 1 of degree equal to the period of the kernel. It is proved that it is necessary and sufficient for the solvability of this problem that a concordance condition (and even a weaker condition) be satisfied (see [4]).Translated from Matematicheskie Zametki, Vol. 12, No. 1, pp. 91–94, July, 1972.The author is thankful to A. V. Yakovlev for his valuable advice.When this article was in press, the author proved that Theorem 1 is valid even without Condition IV. He has also found an example showing that Condition III cannot be discarded.     

Support d'un processus de réflexion

Summary Let D be a regular open set in ⁿ. We describe in this paper the support of ¯D-valued diffusion processes with Reflecting Boundary Condition, generalizing the results of Stroock and Varadhan obtained when D = Ø.     

双调和方程边值问题正解的研究

本文以不动点原理为主要工具 ,证明了一类双调和方程正解的存在性 .     

一类拟线性椭圆型方程在各向异性Соболев空间中非平凡解的存在性

本文借助没有P.S.条件的广义越山引理证明了一类拟线性椭圆型方程在各向异性空间中的非平凡解的存在性。     

Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

In this paper, we consider a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique positive solution to the system with positive initial value, and mainly investigate the long time behavior of the system. Condition for the system to be extinct is given and persistent condition is established. At last, numerical simulations are carried out to support our results.     

广义Kannan型压缩条件的注记

本文给出了 [4 ]中的广义Kannan型压缩条件下映象的一个不动点定理 ,说明了 [2 5]中广义Kannan型压缩条件下映象与 [1 ]中Kannan型压缩条件下映象具有一致的不动点存在性 .     

On the stability of the high-order Higdon Absorbing Boundary Conditions

The Higdon sequence of Absorbing Boundary Conditions (ABCs) for the linear wave equation is considered. Building on a previous work of Ha-Duong and Joly, which related to other forms of boundary conditions, the Higdon ABCs are proved to be energy-stable (on the continuous level) up to any order. This type of stability is stronger than the more standard notion of stability of initial boundary value problems in the sense of Kreiss; in particular it leads to stability estimates which are uniform in time. In consequence to the theorem proved here, energy-stability is immediately implied for the high-order Givoli-Neta and Hagstrom-Warburton ABCs, which are reformulations of the Higdon ABCs using auxiliary variables. A weakness of this theory is that it requires sufficiently smooth data, and that the required smoothness level increases with the order of the ABC. This issue and its implications are discussed.