中国科学技术大学学报 ›› 2019, Vol. 49 ›› Issue (8): 620-624.DOI: 10.3969/j.issn.0253-2778.2019.08.004
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徐建中
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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.
关键词: 非线性, 分数阶微分方程, 激波
Abstract: 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.
Key words: nonlinear, fractional order differential equation, shock wave
徐建中，汪维刚，莫嘉琪. 非线性非局部奇摄动分数阶方程Cauchy问题的激波解[J]. 中国科学技术大学学报, 2019, 49(8): 620-624.
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链接本文: http://just-cn.ustc.edu.cn/CN/10.3969/j.issn.0253-2778.2019.08.004
http://just-cn.ustc.edu.cn/CN/Y2019/V49/I8/620
