DEFORMING METRICS WITH POSITIVE CURVATURE BY A FULLY NONLINEAR FLOW

By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈Γk.     

CONVERGENCE RATES TO NONLINEAR DIFFUSIVE WAVES FOR SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEM

This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of classical solutions is proven,and L~p convergence rates are obtained. Compared with the results obtained by Hsiao and Liu, better convergence rates are obtained in this article.     

EXACT SOLITRAY WAVE SOLUTIONS AND SINGULAR SOLUTIONS TO THE TWO-DIMENSIONAL NONLINEAR DISSIPATIVE-DISPERSIVE SYSTEM

IIntroductlonIntegrMle systems;both classical ajnd quantum me山anies,are aMclnatingsubject·Decades ofresearch In this areahave led to mathematical developme血s that are quite beau－tiful．However,not ail systems posed in physics are Integrable,M Instajnce,the Korteweg－deVies－Burgers(KdV－Burgers),Kur。ot。SI、hinsky(KS)and ifth－order dispersi、Kortevegde Vries(ifth－order KdV)eqUatio。 Therefore the direct methods to sol。nonlinear systemsppear to be more important．In this paper…     

EVANS FUNCTIONS AND INSTABILITY OF A STANDING PULSE SOLUTION OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS

In this paper, we consider a nonlinear system of reaction diffusion equations arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing pulse solutions) and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equations. The Evans functions for the standing pulse solutions are constructed explicitly.     

THE NONLINEAR STABILITY OF TRAVELLING WAVE SOLUTIONS FOR A REACTING FLOW MODEL WITH SOURCE TERM

1IntroductionConsidertilefollowingsystemtlwiwasproposedin[91todescribereactinggasinwhichthereealsttwo"lodes.Where,pcistiledensityofthemajormodeandpsisOftheminormode,f s=1.uisthevelocity,andp=PC'(r as)ispressurewhichcanbederivedbyAvogadro'sLaw.Here,cisthesoundspeedofthemajormode.TheParameterPprovidessometenuouslinkwithrealphysics.Sisthesollrcetermwhere,risareactiontime,rE(p)alldSE(P)areequilibriumdistributions.Thereaderisrefere(lto[9]formorephysicsandnumericalbackgroulld.TheLagrangianform…     

SOLVABILITY OF A THREE-POINT BOUNDARY VALUE PROBLEM WITH NONLINEAR GROWTH

In this paper, we study the existence of solutions to a three-point boundary value problem with nonlinear growth. Sufficient conditions for the existence of solutions to the system in the resonance and non-resonance cases are established by employing Leray-Schauder continuation theorem and the coincidence degree theory.     

一类非线性系统解的有界性

研究了一类非线性微分系统解的有界性 ,所获结果可应用于Li啨ｎａｒｄ类型的方程 ,改进与扩展了众多已有文献中的结果     

非线性方程组的一种解法

文中给出了求非线性方程组的一种解法；它找到一个变换，可使原方程组变换成一个新的方程组，通过求变换后方程组的解求得原方程组的解．     

一类非最小相位非线性系统的鲁棒输出调节

研究了一类具有非最小相位和非线性外部系统的非线性系统的全局鲁棒输出调节问题.首先,利用浸入系统设计了一个非线性内模.其次,把原系统的全局鲁棒输出调节问题转化为增广系统的全局鲁棒镇定问题.然后,利用改变能量函数和动态增益技巧设计了一个状态反馈控制器,使得闭环系统的解有界并且跟踪误差渐近趋于零.最后,利用仿真结果验证了所设计的控制器的有效性.     

非线性灰色离散系统零解的稳定性

本文用区间矩阵和Ｌｙａｐｕｎｏｖ第二方法讨论了具有非线性扰动项的灰色离散系统的稳定性，得到了若干稳定性的代数判据，这些结果将文（５）的主要结果由线性推广到了非线性，并给出了实现的例子。     

CONVERGENT AND DIVERGENT SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR DIFFERENCE SYSTEM

In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form (?)xn+1=anxn+bnf(yn), yn=cnyn-1+dng(xn). We classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can he applied to certain difference systems.     

一类非线性抛物方程组解的爆破时间上下界估计

本文研究了一类非线性抛物方程组uj/t=△uj+fj(u)解的爆破时间的估计问题.通过构造恰当的辅助函数和建立一系列微分不等式,获得了此类非线性抛物方程组解的爆破时间上下界的估计.从而将单个方程的结论推广到了方程组的情形.     

带非线性边界条件的反应扩散方程的数值方法

１引言近年来关于非线性抛物型方程数值解法的研究取得了许多好的结果,其中以Ｃ．Ｖ．Ｐａｏ为主的研究者们利用上、下解方法对带线性边界条件的半线性抛物型方程的有限差分系统进行了广泛的研究,提出了一系列有效的迭代算法（见［１］、［２］、［３］、［４］）．但对带非线性边界条件的半线性抛物型方程初边值问题,作者至今尚未见到有研究者将上、下解方法用在相应的差分系统上,求得数值解．其主要原因是由于边界上函数的非线性,解在边界网格点上的值未知且无法用内部网格点上的值直接表示,相应的差分系统表示形式受到影响,边界网…     

完全非线性伪抛物组的非均匀网格差分格式

完全非线性伪抛物组的非均匀网格差分格式韩永前，袁光伟，周毓麟（北京应用物理与计算数学研究所）ＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＳＷＩＴＨＮＯＮＵＮＩＦＯＲＭＭＥＳＨＥＳＦＯＲＦＵＬＬＹＮＯＮＬＩＮＥＡＲＰＳＥＵＤＯ－ＰＡＲＡＢＯＬＩＣＳＹＳＴＥＭＳ￥Ｈ...     

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO A SECOND-ORDER NONLINEAR DIFFERENCE SYSTEM

In this paper, by the critical point theory, a sufficient condition for the existence of multiple periodic solutions to a nonlinear second order difference system is obtained. An illustrative example is given. Our results improve and generalize some known ones.     

四阶非线性常微分方程非线性两点边值问题解的存在唯一性

本文利用Ｂｏｌｚａｎｏ定理，给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题（１）（２）２，（１）（２）３存在解与存在唯一解的一般性结果，并将所得结果应用于Ｌｉｐｓｃｈｉｚ方程，对Ｌｉｐｓｃｈｉｔｚ方程满足边界条件（２）２，（２）３的边值问题给出了存在解与存在唯一解的具体的充分条件。     

广义混合非线性Schr？dinger方程的拟谱方法

本文讨论了广义混合非线性Schrodinger方程的周期初值问题,构造了守恒的半离散Fourier拟谱格式,对其近似解进行了先验估计,并证明了格式的收敛性.证明了该方程存在孤立子解,并给出其孤立子解的精确表达式.研究了线性化方程的稳定性问题,即在初值有扰动的情况下,该方程只有振荡解和鞍点.最后,通过数值例子验证了格式的可信性,数值计算表明,本格式时间方向可取大步长且是长时间稳定的,我们还计算了孤立子解,并绘出了在初值有扰动的情况下,相空间的轨线图.     

一类非线性非自治系统周期解的存在性

本文给出了系统ｄｘ／ｄｔ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ），ｇ∈Ｒ‘，ｘ∈Ｒ＾Ｎ，ω周期解存在的充分条件，推广了文「１」中的Ｋｒａｓｎｏｓｅｌｓｋｉｉ的结果。     

非线性抛物组非均匀网格差分解的唯一性和稳定性

１．引言 １．对一维非线性抛物组,在文献山中已构造一般非均匀网格差分格式,其中差分逼近的组合系数对不同的网格点和不同的网格层可以不同,并且运用不动点原理证明了差分解的存在性和收敛性．在非均匀网格差分格式中差分逼近的组合系数为常数的情形,文献［２］证明了具有有界二阶差商的离散向量解的存在性、唯一性和稳定性．本文将对文献［１］中构造的一般非均匀网格差分格式,证明所得到的差分解的唯一性和稳定性． 考虑如下非线性抛物组其中是未知的ｍ－维向量函数是给定的矩阵函数,ｊ（ｘ,ｔ,ｕ,ｐ）。是给定的ｍ－维向量函数…     

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic travelingwaves for a class of nonlinear dispersive partial differential equations.By using the bifurcationtheory of dynamical systems to do qualitative analysis,all possible phase portraits in theparametric space for the traveling wave systems are obtained.It can be shown that the existenceof a singular straight line in the traveling wave system is the reason why smooth solitary wavesolutions converge to solitary cusp wave solution when parameters are varied.The differentparameter conditions for the existence of solitary and periodic wave solutions of different kindsare rigorously determined.