摘要
主要研究一类奇异摄动反应扩散方程周期解的存在性和渐近稳定性.首先,利用边界层函数法,构造出形式渐近解,基于微分不等式理论,得到了周期解的存在性.然后讨论周期解在李雅普诺夫意义下的渐近稳定性.最后,由具体例子说明该方法的有效性.
The existence and asymptotic stability of periodic solutions for a sin- gular perturbed reaction-diffusion equation are considered. The formal asymptotic solution is constructed by using the method of the boundary function and the exis- tence of a periodic solution is proved by using the theory of differential inequalities. Moreover, the asymptotic stability of the periodic solution is studied. Finally, an example is presented as an illustration.
出处
《应用数学与计算数学学报》
2018年第1期115-124,共10页
Communication on Applied Mathematics and Computation
基金
上海市自然科学基金资助项目(15ZR1400800)
关键词
奇异摄动
反应扩散方程
周期解
微分不等式
singular perturbation
reaction-diffusion equation
periodic solution differential inequalities
