摘要
奇摄动问题有很强的自然科学的背景,它在生态环境、大气物理、海洋科学、催化反应、激波和量子物理中都有很广泛的应用.本文研究了一类带有小延迟的微分—差分反应扩散方程初值问题.在适当的条件下,利用奇摄动伸长变量法,构造了问题的形式渐近解.再用微分不等式理论证明了解的一致有效性.
The singularly perturbed problems are very strong background in the natural science. There are general applications in the entironment, atmospheric physics, oceanic science, catalyzed reaction, shock wave and quantum physics. In this paper, a class of differentialdifference reaction diffusion equations with a small time delay is considered. Under suitable conditions and by using method of the stretched variable, the formal asymptotic solution is constructed. And then, by using the theory of differential inequalities the uniformly validity of solution is proved.
出处
《数学进展》
CSCD
北大核心
2009年第2期227-232,共6页
Advances in Mathematics（China）
基金
Supported by the National Natural Science Foundation of China(No.40676016)
the National Key Project for Basics Research(2003CB415101-03 and 2004CB418304)
the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)
in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004).
关键词
非线性
反应扩散
奇摄动
时滞
渐近解
nonlinear
reaction diffusion
singular perturbation
time delay
asymptotic solution
