分数阶奇摄动非线性方程的激波层渐近解  

The shock wave layer asymptotic solution for fractional order singularly perturbed nonlinear equation

作　　者：欧阳成[1] 林万涛[2] 莫嘉琪[3] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000 [2]中国科学院大气物理研究所,大气科学和地球流体力学数值模拟国家重点实验室,北京100029 [3]安徽师范大学数学系,安徽芜湖241003

出　　处：《华中师范大学学报（自然科学版）》2016年第3期326-330,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(41275062);浙江省自然科学基金项目(LY13A010005);安徽高校自然科学基金项目(KJ2015A418;KJ2015A347)

摘　　要：研究了一类奇摄动非线性分数阶微分方程初值问题.在适当的条件下,首先求出了原问题的外部解.其次利用伸长变量和幂级数展开理论构造出问题解的激波层和初始层校正项,并得到了解的形式渐近展开式.最后利用微分不等式理论,讨论了问题解的渐近性态,证明了得到的展开式是原问题解的一致有效的渐近估计式.A class of the initial value problem for the nonlinear singularly perturbed fractional order differential equation is considered.Under the suitable conditions,the outer solution of the original problem is obtained.Then,using the stretched variable and expanding theory of power series,the shock layer and initial layer correction terms are constructed,and the formal asymptotic expansion of solution is obtained.Furthermore,with the theory of differential inequalities,the asymptotic behavior of solution for the problem is studied and the uniformly valid asymptotic estimation is proved.

关 键 词：非线性 分数阶方程 奇摄动 

分 类 号：O175.14[理学—数学]