本文证明了求解周期区域上的二阶线性偏微分方程的一致有效渐近解的正交条件是充分和必要的。
In this paper, We prove that the orthogonal condition to solve the uniform asymptotic solution of second order linear P. D. E in periodic region is the necessary and sufficient condition.
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.
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.
其次，一种数值阶验证技术证实求得的二阶渐近解对小参数都是一致有效的。
Secondly, a technique of numerical order verification was applied to verify that the asymptotic solutions were uniformly valid for small parameter.
给出了利用渐近解公式，由模有效折射率的测量值确定波导表面折射率和扩散深度的方法。
A method is given for determining the parameters of a diffused waveguide from the observable values of mode efficient index by using the asymptotic solution equations.
利用微分不等式理论，得到了原初始边值问题解的一致有效的渐近解。
The uniformly valid asymptotic solution to the original initial boundary value problems was obtained by the theory of differential inequalities.
构造出边值问题的解的一致有效渐近近似式。并研究了非共振的情形。
The uniformly valid asymptotic approximations of solutions have been constructed. We also study the case which does not exhibit resonance.
本文讨论了一个奇摄动催化反应问题，得到了问题的形式渐近解，证明了它的一致有效性。
In this paper, a singularly perturbed catalytic reaction problem is considered. The formal asymptotic solution is obtained and its uniform validity is proved.
本文用适当的多项式函数近似扩散光波导的高斯折射率分布函数，推导了导模有效折射率的解析形式渐近解。
The Gaussian index profile of a diffused optical waveguide is approximated by an appropriate polynomial, and the asymptotic solutions of the mode efficient index is derived in a analytical form.
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.
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.
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.
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