条件方程

In this paper, on the base of paraxial approximations, we present a set of absorbing boundary conditions of 3D elastic wave equations and apply to the 3D elastic wave numerical modeling in isotropic medium.

本文基於傍轴近似法提出了计算三维弹性波方程的吸收边界条件公式，表示了各边界面、边棱和角点处波场所满足的单程波方程，并在三维弹性波数值模拟中进行了应用。

Based on two-dimensional elastic wave equation and adopts the well logs as constraint condition, a new imaging method of crosswell seismic data-elastic wave equation inversion and imaging with the well logs constraint is given by using adjoint theory of distribution-parameter control system.

基于二维弹性波动方程，利用分布参数控制系统的伴随理论，采用测井资料作为约束条件，本文给出了一种井间地震资料速度成像的新方法——井间测井约束弹性波动方程反演成像。

In the last chapter,we study the control problems of the distributedparameter system governed by a class of higher order pseudohyperbolicequation related to the symmetric regularized long wave equation.we havediscussed the controllability and optimal control problems.we have obtainedcompatibility condition of the constraint when the state is controllable,therepresentation of the optimal control for both the time optimal control problemand the optimal control problem of minimum energy type,and the equationsatisfied by the minimum time.we have shown that the optimal control belongsto the boundary of the admissible control set.

在第六章中，我们研究了与对称正则长波方程相关的一类高阶拟双曲型方程支配的分布参数系统的控制问题。讨论了系统的状态能控性问题和最优控制问题，给出了状态能控时的约束相容性条件，给出了最速控制问题、最小能量型最优控制问题的最优控制表达式和最速时间所满足的方程式，证明了最优控制属于控制集合的边界。

Basing on the nonatationary linear mild-slope equation developed by Hong Guangwen in 1995, a complete wave model is built considering the bottom friction, nonlinear dispersion relation, and allied reflection and diffraction of several islands. Integrating with corresponding physical and imaginary boundaries, it is solved through Alternating Direction Implicit difference method.

本文以洪广文(1995)推导的非定常线性波缓坡方程为基础，建立考虑底摩阻项，非线性弥散关系，及多岛屿绕射反射作用的缓坡方程求解模式，采用经典的ADI法差分格式，结合物理和虚拟边界条件进行求解。

The structure of analytic solution space is obtained and general form of the analytic solution is presented by means of Dirichlet Series. The convergence of Dirichlet Series solution is discussed.

根据比例延迟微分方程的性质，我们构造了Dirichlet级数形式的解析解，证明了Dirichlet级数形式解的收敛性，获得了保证方程解析解渐近稳定的充分条件。

An adaptive grid scheme controlling cell area is used to generated grids in the divergent section of symmetric annular nozzle, and the generated grids are used in the flowfield calculation through the uncoupled way. The elliptic equations are used to generate grids in three dimensional regions of FDN divergent section, the source terms used in the equations employ a mathematical form which is independent of the boundary shape and of the boundary grid point distribution, the free parameters contained in the source terms are determined by the two restraint conditions, the intersection angle of transverse grid lines with boundaries and the local curvature of the transverse grid lines at the boundaries, and the interior grid distribution controlled directly by the grid point distribution assigned on the boundaries is realized, it makes the grid more clustering near the nozzle wall. For the generated grids in the whole computational regions have a good smoothness and orthogonality, the accuracy of calculation in the flowfield is ensured.

对轴对称的环形喷管采用控制网格面积的自适应网格方法对扩散段部分进行了网格生成，并通过非耦合方式应用于喷管的流场计算中；对强制偏流喷管扩散段内的三维区域采用椭圆型方程进行网格生成，方程中的源项采用了与边界形状和边界网格点分布无关的数学形式，源项内的自由参数由横向网格线与边界的交角及横向网格线在边界处的局部曲率两个约束条件来确定，实现了由边界上的网格分布直接控制内部的网格点，使壁面附近具有较密集的网格，并且在整个计算区域内的网格都具有良好的光滑性和正交性，从而保证了流场计算的准确性。

By using the difference inequalities, the asymptotic behavior of solutions to forced nonlinear neutral difference equations is studied.

利用差分不等式研究了具有强迫项的非线性中立型差分方程解的渐近性，得到了方程的解趋于零的充分条件

Global asymptotic stability of a class of nonlinear rational difference equation s was studied by means of setting up an auxiliary equation,so that a sufficient condition was obtained.

运用建立辅助方程的方法研究一类非线性有理差分方程正平衡点的全局渐近稳定性，得到一个充分条件。

By utilizing the auxiliary ordinary differential equation and its solutions, the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method, and abundant new exact solitary wave solutions were obtained under certain conditions.

利用该方程及其解，采用改进的tanh函数展开法研究了第1类和第2类变系数KdV方程，获得了在一定条件下的若干新精确孤波解。

The positive solutions of the equations are given by using method of directstructure in the Banach space.

直接利用构造的方法，在Banach空间给出了方程的正解，建立了一系列比较定理，给出了方程正解存在的充分条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。