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INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES
作者姓名:黄蔚章  陈育森
作者单位:FujianNormalUniversityFuqingBranch,Fuqing,Fujian350300,P.R.China
基金项目:ScientificResearchProjectofFujianProvinceEducationDepartmentofChina(JB0 0 0 40 )
摘    要:The initial layer phenomena for a class of singular perturbed 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 Norder approximate expansion of perturbed solution concerning small parameter is obtained, and the “ multiple layer“ phenomena of perturbed solutions 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.

关 键 词:渐近线展开  单数微扰  非线性微分方程  初值
收稿时间:3 March 2002

Initial layer phenomena for a class of singular perturbed nonlinear system with slow variables
Huang?Wei-zhang,Chen?Yu-sen.INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES[J].Applied Mathematics and Mechanics(English Edition),2004,25(7):836-844.
Authors:Huang Wei-zhang  Chen Yu-sen
Institution:Fujian Normal University Fuqing Branch, Fuqing, Fujian 350300, P.R. China
Abstract:The initial layer phenomena for a class of singular perturbed 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 solutions 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. Foundation items: Scientific Research Project of Fujian Province Education Department of China (JB00040) Biography: HUANG Wei-zhang (1946≈)
Keywords:singular perturbation  initial layer  asymptotic expansion
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