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The result indicates that the damping term drastically changes the asymptotic behavior of the hyperbolic equation.

分析结果表明，阻尼项强烈地改变双曲型方程解的渐近行为，强阻尼双曲型方程组的能量E随时间按指数衰减，即E≤Cexp。

For this method, although the variable time steps can be employed and the initial conditions can be determined in a more natural way, it investigated a special kind of hyperbolic equation with separable coefficients.

该方法虽然不受等时间步长的限制，对初始条件的选取也更具灵活性，但是它是针对一类变量分离系数型的特殊双曲型方程进行讨论的，对一般形式的双曲型方程则没有提及。

This paper analysed every solving method of Arps Hyperbolic decline equation,pointed out their respective shortcomings, and them presented a new method which solves equation.

对J.J.Arps双曲递减方程各种求解方法进行了分析、研究，指出了各自的不足，同时提出了方程求解的一种新方法。

Parameter τ＇(ratio of lag time of diffusion process to relaxation time of polymer) can define the form of the differential equation: hyperbolic or parabolic.

参数τ＇（扩散的瞬态过程引起的滞后时间与松弛时间之比）的存在与否决定了方程是双曲型还是抛物型。

The finite element and Newmark methods are employed to calculate the temperature field with thermal shock, and the wave effect of heat transfer implied by the hyperbolic equation is evaluated in detail.

采用有限元离散和Newmark方法计算热冲击温度场，并总结了采用二次波动方程产生的波动效应。

First, it is theoretically proved that the correction velocity based on the hyperbolic equation increased along with the increased offset in horizontal layered medium and then the case of horizontal layered medium is analyzed.

首先从理论上证明水平层状介质中基于双曲方法的动校正速度随着炮检距的增大而增大；然后以水平层状介质为例进行了分析。

Special considerations are given to spatial discretization of hyperbolic equation with non self-adjoint operator nature.

同时构造了一个用于求解此耦合过程的统一混合弱形式，并且针对其中具有非自伴随算子特性的双曲线控制方程的空间离散进行了特殊考虑。

The calculation result shows the velocity of heat and mass transfer is finite and has the characteristics of wave. The compare of the results of hyperbolic equation and those of parabolic equations shows there is a delay between both the thermal and the mass of the former and those of latter.

计算结果表明：在考虑热量传递过程的松弛效应以后，发现热量传递速度是有限的且具有明显的波传播机制，计算结果和由抛物型方程进行计算得到的结果进行比较发现不管是热量传递还是质量传递在时间上都有一个延迟。

Chapter 2 considers an AD Galerkin method with moving finite element spacesfor a class of second-order hyperbolic equation.

第二章讨论一类二维二阶双曲型方程的交替方向变网格Galerkin有限元方法。

The solution to the one dimensional hyperbolic runoff equations and sediment equation are obtained respectively by using the characteristics method and finite difference method.

利用水力学原理建立了坡面降雨径流和土壤侵蚀模型，分别采用特征线法和有限差分法对径流量和土壤侵蚀量进行了求解，并针对具体降雨事件进行了模拟计算，计算结果与试验小区实测值基本一致。

Who? I never heard of him, Paul said, before asking teammate James Posey if he had heard of him.

赛后，科比说，他一直都是一名非常出色的射手，今天他打得很棒。

When I joined the company, I rotated around the different sections.

我加入这个公司时，轮换过几个不同的部门。