ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER－STOKES EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＴＨＥＳＯＬＵＴＩＯＮＴＯＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＴａｎｇＸｉａｎｊｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．,Ｓｉｃｈｕａｎｕｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ６１００６４...     

SOME NONLINEAR OPERATOR EQUATIONS AND THEIR APPROXIMATE SOLUTIONS

Consider nonlinear operator equation, Ax+Fx=α, where A is a dense closed linear operator, F is a nonlinear operator. In this paper, we shall give the criterion about solution existence of this equation and the convergence criterion of Galerkln approximate solutions.     

APPROXIMATE INERTIAL MANIFOLDS TO THE NAVIER-STOKES EQUATIONS

ＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＴＯＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳ王碧祥兰州大学，邮编：７３００００ＡＰＰＲＯＸＩＭＡＴＥＩＮＥＲＴＩＡＬＭＡＮＩＦＯＬＤＳＴＯＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯ...     

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE VISCOELASTIC EQUATIONS FOR KOITER SHELLS

In this paper,we consider the linearly viscoelastic equations for Koiter shells. Also,we prove the existence and uniqueness of the solution by Galerkin method.     

ON THE EXISTENCE AND UNIQUENESS OF CLASSICAL GLOBAL SOLUTION TO A TYPE OF B0USSINESQ EQUATIONS

The existence and uniqueness of classical global solutions to a type of Boussinesq equations withinitial and boundary values are studied in this paper. The existence of such solutions is proved bymeans of compactness theorem and Schauders fixed point theorem, and its uniqueness by the so calledenergy method.     

ON THE ASYMPTOTIC EXPANSION OF THE SOLUTION OF NON-AUTONOMOUS AND NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

In this paper we will deal with the asymptotic behavior of the solution to a class of non-autonomous and nonlinear differential equations which is more general than the Riccati matrix differential equation.     

ON THE BOUNDEDNESS AND THE STABILITY RESULTS FOR THE SOLUTION OF CERTAIN FIFTH ORDER DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＡＮＤＴＨＥＳＴＡＢＩＬＩＴＹＲＥＳＵＬＴＳＦＯＲＴＨＥＳＯＬＵＴＩＯＮＯＦＣＥＲＴＡＩＮＦＩＦＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＣＥＭＩＬＴＵＮＣ（ＹｕｚｕｎｃｕＹｉｌＵｎｉｖｅｒｓｉｔｙ，Ｅｇ...     

ON THE IDENTIFICATION OF COEFFICIENTS OF SEMILINEAR PARABOLIC EQUATIONS

ＯＮＴＨＥＩＤＥＮＴＩＦＩＣＡＴＩＯＮＯＦＣＯＥＦＦＩＣＩＥＮＴＳＯＦＳＥＭＩＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＬＩＵＺＨＥＮＨＡＩ（刘振海）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈａｎｇｓｈａＵｎｉｖｅｒｓｔｔｙｏｆＥｌ...     

APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS AND CONVOLUTION INTEGRALS USING LEGENDRE POLYNOMIALS

It has been argued that Chebyshev polynomials are ideal to use as approximating functions to obtain solutions of integral equations and convolution integrals on account of their fast convergence. Using the standard deviation as a measure of the accuracy of the approximation and the CPU time as a measure of the speed, we find that for reasonable accuracy Legendre polynomials are more efficient. '     

THE TRAVELING WAVE SOLUTIONS AND APPROXIMATE SOLUTIONS FOR BOUSSINESQ EQUATIONS

First, all possible traveling wave solutions of the Boussinesq equations in shallow water theory are discussed. It is shown that these solutions are periodic waves, convex solitary waves and concave solitary waves. Second, by using a reductive perturbation method, shallow water equation with a small damping term have been reduced to a single KdV-Burgers equation, from which the approximate solution of the original equations can be expressed.     

二阶完全非线性蜕化抛物方程

本文研究了一个空间变量的二阶完全非线性蜕化抛物方程ｕｔ＝Ｆ（ｕｘｘ，ｕｘ，ｘ，ｔ）的第一边值问题。在仅要求Ｆ及其一阶导数满足结构条件的情形，给出了蜕化问题连续解的存在唯一性。这个工作将渗流方程的结果推广到非常一般的情形。     

一类拟线性抛物方程的均匀化

本文研究具有振荡系数的二阶抛物方程δｔｂ（ｕ）－δｘｉ（αｉｊ（ｘ／ε）δｘｊｕ＋αｉ（ｂ（ｕ）））＝ｆ（ｂ（ｕ））的渐近性态。由于函数ｂ（ｕ）的导函数ｂ‘（ｕ）允许为非线性函数，并可在ｕ＝０处退化，研究了均匀化问题通常的能量方法在这里行不通。     

Fuzzy矩阵方程的摄动问题

讨论了Fuzzy矩阵A的同解简化矩阵A^(2),指出陈贻源论文《解Fuzzy关系方程》中定量3的错误。研究Fuzzy矩阵方程的摄动问题,解决了汤服成（2000）提出的未解决问题。     

伪抛物型复方程的Riemann─Hilbert初边值问题的可解性及其近似解的误差估计

本文使用参数开拓法证明了非线性伪抛物型复方程在多连通区域上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ初边值问题的可解性，并对近似解作出了误差估计。     

具有临界增长的拟线性椭圆型混合边值问题的非平凡解

本文给出了ＲＮ中一类有界区域εαＮ上临界增长拟线性椭圆型方程Ｆｉ（ｘ，ｕ，Ｄｕ）－Ｆｕ（ｘ，ｕ，Ｄｕ）＝０的混合边值问题非平凡解的存在性。     

高维非线性四阶抛物型方程初值问题全局解

对一类高维非线性四阶抛物型方程初值问题,在初始数据适当小及非线性项适当光滑的情况下,获得了其古典解全局存在性。     

CANONICAL CORRELATION EQUATIONS AND THEIR EXTREMAL PROPERTIES

The canonical variables and canonical correlation coefficients satisfy a matrix equation which is called the canonical correlation equation. There are some different forms of the canonical correlation e-quations given in the literature. In this paper, we discuss four different forms of the canonical correlation equations. The purpose of this paper is to give extremal properties of the solutions of the canonical correlation equations. The results show that canonical variables maximize the determinant of the dispersion matrix of the transformed variables.