具有非零退化根的Cole问题解的渐近分析  

Asymptotic Analysis to Cole Problem with Nonzero Degenerate Solution

作　　者：王爱峰[1,2] 徐梅[1] 徐涵[3] 

机构地区：[1]淮阴师范学院数学科学学院,江苏淮安223001 [2]华东师范大学数学系,上海200241 [3]临沂大学数学系,山东临沂276005

出　　处：《南昌大学学报（理科版）》2010年第6期527-531,535,共6页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11071075)

摘　　要：针对Cole问题中退化根为非零根的几种情况进行了研究,借助Linard变换将所研究问题转化为可以用边界函数法处理的问题,并用边界函数法构造了该问题n阶形式渐近解,用微分不等式理论证明了解的存在性和形式渐近解的一致有效性。By using the transformation of Linard,it studies Cole problem when it has non-zero degenerate solution.The method of boundary functions was used to construct the formal asymptotic solution of this singular perturbed problem.Finally,using the method of differential inequality the existence of solution and the uniform validity of its formal asymptotic solution were proved.

关 键 词：微分不等式 边界函数 上解 下解 

分 类 号：O175[理学—数学]