并得到了一致有效的渐近展开式。
The uniformly valid asymptotic expansion in entire is obtained.
得到了问题解的一致有效的渐近展开式。
The uniformly valid asymptotic expansion of solution for the problem is obtained.
重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。
Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.
基于基本方程组和高玉臣、黄克智提出的应力场的渐近展开式作了渐近分析。
On the basis of the governing equations and the asymptotic expansion of the stress fields proposed by Gao and Hwang, a generally asymptotic analysis is performed.
研究了一类ENSO摄动模型。利用摄动理论和方法，构造了相应问题的渐近展开式。
A class of ENSO perturbed model is studied. Using the perturbation theory and method, the asymptotic expansions of solution of corresponding problem are constructed.
在一般的条件下，证明了解的存在性，而且得到解及其各导数的高阶一致有效渐近展开式。
Under the general conditions, we prove the existence of the solution and get the asymptotic expansions of the solution and its derivatives, which are uniformly valid for the higher orders.
第五章讨论二维蜂窝结构热方程边值问题，给出了一个多尺度渐近展开式和有限元计算格式。
In Chapter 5, we study the multi-scale finite element method for the heat equation of composite materials with honeycomb structure in two dimension domain.
首先讨论了隐差分解与显差分解的关系，并利用差分解的渐近展开式构造差分校正解来提高精度。
The relation between the explicit difference solution and the implicit one is established. A correction difference solution with higher accuracy is constructed by the use of asymptotic expansion.
我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.
利用不动点原理及微分不等式理论，我们证明了边值问题解的存在性，并给出了解的一致有效渐近展开式。
Using the fixed point principle and the theory of differential inequality, we prove the existence of the solution and an uniformly valid asymptotic expansions of the solution is given as well.
本文最后给出，当角频率有偏离时，其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。
If a parameter in the inputs of the original large scale system deviates, the corresponding reduced order model can be changed by using the asymptotic expansion of the input functions.
其收敛性的证明是依据其渐近扩散展开式，在边界层上得到的误差估计逼近其离散纵标方法的解。
Our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete-ordinate method.
然后，运用微分不等式理论，证明了形式渐近解的一致有效性，并得出了解得任意阶的一致有效展开式。
And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.
然后，运用微分不等式理论，证明了形式渐近解的一致有效性，并得出了解得任意阶的一致有效展开式。
And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.
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