非线性非局部奇摄动分数阶方程Cauchy问题的激波解  

The shock wave solution to nonlinear nonlocal singularly perturbed fractional order equation Cauchy problem

作　　者：徐建中 汪维刚 莫嘉琪 XU Jianzhong;WANG Weigang;MO Jiaqi(Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China;Department of Basic, Hefei Preschool Education College, Hefei 230011, China;School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003, China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]合肥幼儿师范高等专科学校基础部,安徽合肥230011 [3]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《中国科学技术大学学报》2019年第8期620-624,644,共6页JUSTC

基　　金：the National Natural Science Foundation of China(41275062);the Key Program of the Excellent Young Talents Support of Higher Education in Anhui Province(gxyq2018116);the Natural Science Foundation of the Education Department of Anhui Province(KJ2017A704,KJ2017A901,KJ2018A0964,KJ2019A1261,KJ2019A1303);the Teaching Groups in Anhui Province(2016jytd080)。

摘　　要：研究了一类非线性非局部奇摄动分数阶方程Cauchy问题.首先求出了原Cauchy问题的外部解.然后利用伸长变量、合成展开法构造出解的激波层和初始层校正项.最后利用微分不等式理论,研究了原非线性非局部奇摄动分数阶方程Cauchy问题解的渐进性态并证明了它的一致有效的渐近估计式.A class of Cauchy problem for the nonlinear nonlocal singular perturbation fractional order equation was considered.First,the outer solution to the original Cauchy problem was obtained.Then,using the stretched variables and the composing expansion method the shock wave layer and initial layer were constructed.Finally,using the theory of differential inequality the asymptotic behavior of the solution to the original Cauchy problem of nonlinear nonlocal singular perturbation fractional order equation was studied and its uniformly valid asymptotic estimation was proved.

关 键 词：非线性 分数阶微分方程 激波 

分 类 号：O175.14[理学—数学]