摘要
研究了一类具有两个小延迟的微分差分方程初值问题的渐近解,这里两小迟滞为不同量级的小参数,首先在一定的条件下构造了初值问题的包含外部解和边界层的幂级数展开式;然后利用原问题的退化形式先求出外部解,再利用不同的伸长变量,依据边界层特有的性质,分别计算出两种量级下该初值问题的边界层,从而得到两种情形下的渐近解,发现边界层都具有阶梯结构.
The asymptotic solutions of a initial value problem about a class of differential difference equations with two small delays are studied. Here , two small delays are small parameters of different orders of magnitude . A power series expansion consisting of the outer solution and the boundary layer of the initial value problem are constructed firstly under the certain conditions. Then the outer solution is given by the degenerate form of the original probh＇m. Finally by various stretched variables, according to the nature of the boundary layers, the boundary layers of two orders of magnitude of the initial value problem are given respectively. So, the asymptotic solutions of two cases are obtained. The boundary layers are both found staircase structure.
出处
《应用数学学报》
CSCD
北大核心
2014年第3期407-413,共7页
Acta Mathematicae Applicatae Sinica
基金
安徽省高校优秀青年人才基金资助项目(2012SQRL037)
关键词
奇摄动
两参数
小延迟
singular perturbation
two parameters
small delay equations
