双参数奇摄动非线性抛物型系统的广义尖层解

The Generalized Spike Layer Solution to Singular Perturbation Nonlinear Parabolic System with Two Parameters

本文研究了一类非线性抛物型微分系统的奇异摄动问题.首先利用奇异摄动方法构造了外部解.其次,分别采用多尺度法和伸长变量法获得尖层校正项、边界层校正项和初始层校正项.最后得到了广义解的渐近展开解.利用不动点定理证明了渐近解的一致有效性.该渐近解可用于对广义解进行解析运算,可以了解其更多的特征,因此具有较好的应用前景.

A nonlinear parabolic differential system to the singular perturbation problem is studied in this paper.First the outer solution is structured by using the singular perturbation method.Second the spike layer corrective,boundary layer corrective and initial layer corrective terms are obtained by using the multiple scales and stretched variable methods respectively.Final the asymptotic expansion of the generalized solution is obtained.Using the fixed point theorem,the uniform validity for the asymptotic solution is proved.And the asymptotic solution can also carry on analytical operation.So it is known more characters for the generalized solution.Thus it possesses better applied foreground.