EXACT SOLUTIONS OF THE VARIABLE COEFFICIENT KdV AND SG TYPE EQUATIONS

In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied. The exact solutions of the KdV and SG equations are obtained. In particular,the soliton solutions oftwo equations are found.     

PINNING OF VORTICES FOR THE GINZBURG-LANDAU FUNCTIONAL WITH VARIABLE COEFFICIENT

In this paper, the asymptotic behavior as ε→O of the minimizers u,of the Ginzburg Lan-dau functional with variable coefficient is discussed. The singularities are found to be located at thepoints which globally minimize the coefficient. The zeros of u, are accumulated near the singulari-ties as is small enough. This verifies the pinning mechanism.     

D''''ALEMBERT FORMULA AND THE DIRECT OR INVERSE PROBLEMS FOR WAVE EQUATION

In this paper, a new proof of D'Alembert formula for Cauchy problems of wave equation is proposed. And some D'Alembert-type formulas for Cauchy problem with discontinuous coefficients on semi-infinite initial boundary value problem are proposed. Based on above discussion, the c(?)racteristics methods for the direct and inverse problems of the stress wave equation for uniform layerad elastic medium are investigated. The aim of this paper is to stress the significance and application of the characteristics concept and approach.     

BAYESIAN VARIABLE SAMPLING PLAN FOR THE WEIBULL DISTRIBUTIONWITH TYPE Ⅰ CENSORING

1.IntroductionAnimportsnttopicinQualityColltrolisthestudyofacceptancesamplingplan.Foravariablesamplingplan,thequalityofanitemismeasuredbyarandomvariable.Todesignavariablesamplingplanistodeterminethesamplesizeandthespecilicstionlicit(s).Manyschemeshav...     

ON THE USE OF THE PAINLEV PROPERTY FOR OBTAINING MIURA TYPE TRANSFORMATION

We present a method for obtaining an associated hierarchy of evolution equations possessingthe Painleve property from a given hierarchy which possesses the Painleve property. This method isapplied to the classical Boussinesq hierarchy to obtain the Miura type transformation and themodified classical Boussinesq hierarchy. It is also used to construct a large hierarchy of evolutionequations which possess the Paiuleve property and include the classical Boussinesq the JaulentMiodek, the dispersive long wave hierarchy as special cases. All these hierarchies have the samemodified hierarchy.     

BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

In this article, the author studies the boundedness and convergence for the non-Lienard type differential equation (x|·)=a(y)-f(x) (y|·)=b(y)β(x)-g(x) e(t) where a(y),b(y),f(x),g(x),β(x) are real continuous functions in y∈R or x∈R,β(x)≥0 for all x and e(t) is a real continuous function on R = {t: t≥0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.     

ON THE SINGULAR CA UCHY PROBLEM FOR NONLINEAR EQUATION OF HYPERBOLIC TYPE

Denote Ω={(x,y)|x>y}. We consider in Ω the Cauchy problem for the nonlinear singular equation:     

THE INVOLUTIVE REPRESENTATION OF THE SOLUTION FOR THE COUPLED BURGER－MKDV EQUATION

ＴＨＥＩＮＶＯＬＵＴＩＶＥＲＥＰＲＥＳＥＮＴＡＴＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮ　ＦＯＲＴＨＥＣＯＵＰＬＥＤＢＵＲＧＥＲ－ＭＫＤＶＥＱＵＡＴＩＯＮ￥ＺｈａｎｇＢａｏｃａｉ（张保才）＆ＧｕＺｈｕｑｕａｎ（顾祝全）（ＳｈｉｊｉａｚｈｕａｎｇＲａｉｌｗａｙ...     

INVERSE SCATTERING PROBLEM FOR ONE-DIMENSIONAL SCHRDINGER OPERATORS RELATED TO THE GENERAL STARK EFFECT

This paper disccusses the inverse scattering problem for one-dimensional Schrodinger operatorsrelated to the general Stark effect. We provide a ganeral framework which can be applied both to theStark-effect operator and the ordinary Schrodinger operator.     

ASYMPTOTIC PROPERTY FOR THE SOLUTION TO THE GENERALIZED KORTEWEG－DE VRIES EQUATION

ＡＳＹＭＰＴＯＴＩＣＰＲＯＰＥＲＴＹＦＯＲＴＨＥＳＯＬＵＴＩＯＮＴＯＴＨＥＧＥＮＥＲＡＬＩＺＥＤＫＯＲＴＥＷＥＧ－ＤＥＶＲＩＥＳＥＱＵＡＴＩＯＮＺＨＡＮＧＬＩＮＧＨＡＩ（张领海）（ＤｅｐｏｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＯｈｉｏＳｔａｔ...     

Sine—Gordon方程的全局吸引子的维数估计

本文得到了阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的狄氏问题的全局吸引子的Ｈａｕｓｄｏｒｆｆ维数以偶数上界的参数条件，特别地，当阻尼与Ｌａｐｌａｅ算子的第一个特征值适当大时，全局吸引子是零维的，零维吸引子恰是系统的唯一平衡解并且指数吸引相空间的有界集。     

Sine-Gordon方程的一类低阶非协调有限元分析

本文讨论了Sine-Gordon方程的一类低阶非协调有限元一般逼近格式,直接利用插值技巧和单元的特殊性质导出了相应未知量的最优误差估计.     

A METHOD FOR SOLVING THE INVERSE SCATTERING PROBLEM FOR SHAPE AND IMPEDANCE

The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.     

SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

1. IntroductionThere has been much discussion recently aboat deswi symplectic numrical schemesfor both finite and idste dimensional Hamilonian systems ([1] - [8]). A dass of syInPlecticsMes for linear wav equations has been sUggested [1], and numerical exPerimellt8 for tlieseschemes have been conducted [8, 9]. Results shOw that the syInPlectic method8 are inhereotlyfree from arttheial dissipatinn and all kinds of nonHtalltoulan pollutions, and are thu8 Of highquality and resolution.In thi…     

二阶变系数椭圆型微分方程谱方法的后验误差估计

As to the posteriori error of spectral method for second order elliptic differential equation of variable coefficient,we construct two easy solvable differential equations of constant coefficient. Among the two energy norms of the solutions of two differential equations, one is larger than the energy norm of exact error ,another is smaller than the energy norm of exact error, and the two energy norms of the solutions are of same order.     

INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES

This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.     

ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA

In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0<γ≤4 and γ相似文献   

MULTISCALE ASYMPTOTIC EXPANSION FOR A CLASS OF HYPERBOLIC-PARABOLIC TYPE EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

In this paper, we will discuss the asymptotic behaviour for a class of hyperbolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.     

带对流项的渗流型方程的显格式

１．引言　假设有一种不可压流体在一均匀的、各向同性的刚性多孔柱形介质中流动,流动沿着与水平方向成ａ角进行,则可用下述方程描述其中λ＝ｓｉｎα,ｕ表示介质的含湿度．λ＝０,即表示沿水平方向流动,它和λ≠０的情形分别称为无对流项和有对流项的渗流方程．它们可分别写成下面一般的形式：　渗流型方程是退化抛物型方程,由于它可有退化点（使二阶导数项系数为零的点）,它与正规抛物型方程有很大区别．正规抛物型方程有充分光滑的古典解,渗流方程则不然．即使初值充分光滑,也不能保证渗流方程有光滑的解．实际上,渗流方程可有…     

反演声波散射区域的一种组合方法

本文用声波远场模式的完全与不完全数据对声波散射区域进行了反演。其前提条件是整体场满足齐次Dirichlet边界条件,对于这个问题,文中给出一种对任意波数k（k〉0）的组合方法。方法的收敛性得到证明,数值例子表明了方法是可行的和精确的。