一类催化抑制系统反应扩散方程的奇摄动(英文)  

Singular Perturbation for Reaction Diffusion Equations of Activator Inhibitor Systems

作　　者：温朝晖[1] 莫嘉琪[2,3] 

机构地区：[1]安徽财经大学统计与应用数学学院应用数学研究所,蚌埠安徽233030 [2]安徽师范大学数学系,芜湖安徽241003 [3]湖州师范学院理学院,湖州浙江313000

出　　处：《数学进展》2012年第4期455-462,共8页Advances in Mathematics（China）

基　　金：supported by NSFC(No.40876010);the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences(No.XDA01020304);the Natural Science Foundation from the Education Bureau of Anhui Province(No.KJ2011A135,No.KJ2011Z003);the Natural Science Foundation of Jiangsu Province(No.BK2011042)

摘　　要：研究了一类奇摄动非线性催化抑制系统反应扩散方程.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、多重尺度和幂级数展开理论构造出解的形式渐近展开式最后利用微分不等式理论讨论了问题解的一致有效性和渐近性态.A class of nonlinear singularly perturbed reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, first, the outer solution of the original problem is obtained; second, using the stretched variable, variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed; and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.

关 键 词：非线性 反应扩散 催化系统 奇摄动 

分 类 号：O175.29[理学—数学]