非线性双重介质模型的精确解及动态特征

考虑了二次梯度项的非线性双重介质模型．在模型中假设岩块和裂缝间的压力差作为初始未知量,在岩块中是拟先态的,从而避免了解联立方程组．利用广义Hankel变换求得了径向流动的解析解,由于解析解是无穷级数,无法得到具体的值．通过数值求解特征值问题,从而算得了窟体的压力值,并探讨了非线性参数和双重介质参数变化时压力的变化规律,给出了典型压力曲线图版,这些结果可用于实际的试井分析．     

分形油藏中非牛顿松弛粘弹性液体广义流动分析

将分形引入渗流力学,建立了分形油藏具有松弛特性的粘弹性液体的不稳定渗流模型;利用双参数（ ｄｆ ,ｄｓ） 刻画分形油藏的分形特性,利用四参数（ｄｆ,ｄｓ ,λｖ ,λｐ） 描述粘弹性液的广义流动特征;提出了广义的正交变换,并利用Ｌａｐｌａｃｅ＿Ｗｅｂｅｒ 变换,拉氏＿正交变换给出了无限大地层和有界地层的精确解和渐近解;通过拉氏数值反演和渐近解分析了分形油藏粘弹性液体流动特征·　探讨了改变分形参数时压力变化规律·     

双非线性抛物组解的有界性

本文考虑对角型双非线性抛物型方程组，在一般结构条件下，证明广义解局部有界和整体有界，并对一特殊情形，证明了如果解在抛物边界为零，那么它只能是零解．     

含外力项的广义KdV方程的新自Darboux变换和显式解析解

基于 Ｒｉｃｃａｔｉ形式的 Ｌａｘ对,本文推得了含外力项的广义 ＫｄＶ方程的新自Ｄａｒｂｏｕｘ变换．当应用这个变换时,仅需要做积分,就能获得一系列显示解析解,其中包含类孤波解．这种途径对于寻找非线性发展方程新的具有物理意义的解或许是有用的．     

无限大多层油藏渗流问题的解析解及其应用

本文对无限大多层油藏有越流的定压生产情形,利用Weber变换方法,给出了产量函数及压力分布函数的解析解.并将计算结果绘成曲线图,这些结果可用于定压生产情形的不稳定试井分试.     

非线性分数微分方程解的若干存在性结论

研究了非线性分数微分方程解的存在性,通过考察非线性项在无穷远处的增长或者非线性项在某个有界集上的“高度”获得了若干新的存在性结论,主要工具是Schauder不动点定理和Leray-Schauder不动点定理．     

具有凹凸非线性项和变号权函数的奇异椭圆系统解的多重性

本文考虑在有界区域上具有凹凸非线性项和变号权函数的奇异椭圆系统解的多重性.在适当的假设条件下,我们使用Nehari流形和纤维映射得到了系统至少有两个非平凡解.     

离散系统的广义同步

讨论两个离散系统之间的广义同步．通过构造合适的非线性耦合项,导出了驱动响应系统获得广义同步的充分条件．在一个正不变的有界集上,许多混沌映射满足这些充分条件．通过3个例子,说明了充分条件的有效性．     

带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性

利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题．该材料的弹性模量和传热系数是可变的．空腔的内表面没有力作用,但有热冲击作用．利用Laplace变换求得直接逼近解．数值求解了Laplace逆变换．给出了温度、位移和应力的分布图．     

S-凸集值映射的次梯度和弱有效解

本文为半序Banach空间的集值映射定义了一种次梯度，证明了集值映射Hahn-Banach定理．应用此结论，本文还讨论了次梯度的存在性以及广义向量最优化问题弱有效解的最优性条件．     

A Class of Quadratic Integral-Differential Equations

A nonlinear integro-ordinary differential equation built up by a linear ordinary differential operator of n th order with constant coefficients and a quadratic integral term is dealt with. The integral term represents the so-called autocorrelation of the unknown function. Applying the Fourier cosine transformation, the integral-differential equation is reduced to a quadratic boundary value problem for the complex Fourier transform of the solution in the upper half-plane. This problem in turn is reduced to a linear boundary value problem which can be solved in closed form. There are infinitely many solutions of the integral-differential equation depending on the prescribed zeros of a function related to the complex Fourier transform.     

双重介质分形油藏渗流问题

将油井有效半径引入双重介质分形油藏渗流问题的内边界之中,从而建立了双重介质分形油藏的一种渗流模型,并在考虑了井筒储集和表皮效应的情况求得了外边界为无限大、有界封闭和有界定压三种情况下双重介质分形油藏压力分布的精确解析表达式,利用拉氏数值反演Stehfest方法分析了双重介质分形油藏压力动态特征,讨论了各种参数对压力动态的影响。     

Semi-analytical method for solving nonlinear heat diffusion problems in spherical medium

A semi-analytical methodology, based on the finite integral transform technique, is proposed to solve the heat diffusion problem in a spherical medium subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The method proceeds by treating the nonlinearity term in the boundary condition as a source in the differential equation and keeping other conditions unchanged. The results obtained from this semi-analytical solutions are compared with those obtained from a numerical solution developed using an explicit finite difference method, which showed very good agreement.     

Finite difference reaction-diffusion systems with coupled boundary conditions and time delays

This paper is concerned with finite difference solutions of a coupled system of reaction-diffusion equations with nonlinear boundary conditions and time delays. The system is coupled through the reaction functions as well as the boundary conditions, and the time delays may appear in both the reaction functions and the boundary functions. The reaction-diffusion system is discretized by the finite difference method, and the investigation is devoted to the finite difference equations for both the time-dependent problem and its corresponding steady-state problem. This investigation includes the existence and uniqueness of a finite difference solution for nonquasimonotone functions, monotone convergence of the time-dependent solution to a maximal or a minimal steady-state solution for quasimonotone functions, and local and global attractors of the time-dependent system, including the convergence of the time-dependent solution to a unique steady-state solution. Also discussed are some computational algorithms for numerical solutions of the steady-state problem when the reaction function and the boundary function are quasimonotone. All the results for the coupled reaction-diffusion equations are directly applicable to systems of parabolic-ordinary equations and to reaction-diffusion systems without time delays.     

General Decay for a Viscoelastic Equation of Variable Coefficients in the Presence of Past History with Delay Term in the Boundary Feedback and Acoustic Boundary Conditions

In this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with relation between the damping term and relaxation function. The second result is given without imposing any restrictive growth assumption on the damping term and the kernel function \(g\). Our result extends the decay result obtained for problems with finite history to those with infinite history.     

Nonreflecting boundary condition for the wave equation

To solve the time-dependent wave equation in an infinite two (three) dimensional domain a circular (spherical) artificial boundary is introduced to restrict the computational domain. To determine the nonreflecting boundary we solve the exterior Dirichlet problem which involves the inverse Fourier transform. The truncation of the continued fraction representation of the ratio of Hankel function, that appear in the inverse Fourier transform, provides a stable and numerically accurate approximation. Consequently, there is a sequence of boundary conditions in both two and three dimensions that are new. Furthermore, only the first derivatives in space and time appear and the coefficients are updated in a simple way from the previous time step. The accuracy of the boundary conditions is illustrated using a point source and the finite difference solution to a Dirichlet problem.     

On the numerical solution of the flow between a rotating and a stationary disk

The flow between two co-axial, infinite disks, one rotating with constant angular velocity and one stationary is treated in this paper. The problem is reduced to that of finding the solution of a two-point boundary value for a sixth order nonlinear ordinary differential equation and three boundary conditions at each of a finite interval. The numerical solutions are obtained by using a fourth order Runge-Kutta integration scheme in modification due to Gill and in conjunction with a modified shooting method to correct the initial guesses at one boundary. The numerical calculations for different Reynolds numbers are carried out. The results obtained by this method are compared with available results. The comparison shows excellent agreement.     

Transient elastodynamic three-dimensional problems in cracked bodies

The general formulation of the transient elastodynamic second boundary value problem in an isotropic linear elastic body with a crack of arbitrary shape by combining the boundary integral equation method and the Laplace transform with respect to time is presented in this paper. Both finite and infinite elastic bodies are considered. A numerical solution of the transformed boundary integral equations is proposed.     

一类抛物方程初边值问题的精确解及其应用

本文建立了多层合采油藏压力分布新模型,并在无限大、有界定压和有界封闭三种边界条件下,求得了均质弱可压缩液体朝向具有井筒储集和表皮效应井渗滤时,各层内压力分布的精确表达式;给出了该压力解在油藏试井分析中的应用.     

Stability with respect to the initial data and monotonicity of an implicit difference scheme for a homogeneous porous medium equation with a quadratic nonlinearity

We study the stability and monotonicity of a conservative difference scheme approximating an initial-boundary value problem for a porous medium equation with a quadratic nonlinearity under certain conditions imposed only on the input data of the problem. We prove a grid analog of the Bihari lemma, which is used to obtain a priori estimates for higher derivatives; these estimates are needed both in the proof of the continuous dependence of the solution on small perturbations in the input data and for the analysis of monotonicity in the nonlinear case. We show that, regardless of the smoothness of the initial condition, the higher derivatives can become infinite in finite critical time. We give an example in which there arises a runningwave solution, which justifies the theoretical conclusions.