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中文摘要：
考虑一类广义两参数非线性双曲型积分-微分方程奇摄动模型.首先,利用广义Fredholm型积分方程,得到了该模型的广义外部解;其次,用多重尺度变量方法得到了广义解的边界层校正项;然后,利用伸长变量方法,得到了广义解的初始层校正项;最后,构造了广义奇摄动解的合成渐近展开式,并用不动点理论证明解的渐近展开式的一致有效性.
英文摘要：
We considered a class of generalized two parameter nonlinear hyperbolic integral-differential equation with singular perturbation model.Firstly,the generalized outer solution of the model was obtained by using the generalized Fredholm type integral equation.Secondly,the boundary layer corrective term of the generalized solution was obtained by using the method of multiple scale variables.Thirdly,the initial layer corrective term of the generalized solution was obtained by using the stretched variable method.Finally,the synthetic asymptotic expansion of the generalized singular perturbation solution was constructed,and the uniform validity of the asymptotic expansion of the solution was proved by using the fixed point theory.
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