Initial Layer Phenomena for a Class of Singular Perturbed Nonlinear System with Slow Variables
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摘要: 研究含有慢变量的一类奇摄动非线性系统初始层现象，通过引进不同量级的伸长变量,构造不同“厚度”的初始层校正项，得到了摄动解关于小参数的N阶近似展开式,揭示了摄动解呈现的“层中层”现象，并利用不动点原理证明了摄动解的存在,给出了解的一致有效的渐近展开式．Abstract: The initial layer phenomena for a class of singular perturbe d nonlinear system with slow variables are studied.By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness",the N-order approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutins are revealed.Using the fixed point theorem,the existence of perturbed solution is proved,and the uniformly valid asymptotic expansion of the solutions is given as well.
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Key words:
- singular perturbation /
- initial layer /
- asymptotic expansion
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[1] 陈育森，黄蔚章.奇摄动非线性系统初值问题的套层解[J].应用数学学报, 2001，24（1）：49—55. [2] 陈育森，黄蔚章.双参数奇摄动非线性系统套层解[A].见:陈树辉等编.现代数学和力学会议文集（MMM-Ⅷ）[C].广州：中山大学出版社，2001，446—451. [3] 林宗池.某类奇摄动边值问题的多重边界层现象[J].福建师大学报（自然科学版）,1993，9(3):15—23. -
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