非线性奇摄动反应扩散问题的广义渐近解  

The generalized asymptotic solution for nonlinear singular perturbation reaction diffusion problem

作　　者：史娟荣[1,2] 陈贤峰[2] 莫嘉琪[3] 

机构地区：[1]安徽机电技术学院,安徽芜湖241002 [2]上海交通大学数学系,上海200240 [3]安徽师范大学数学系,安徽芜湖241003

出　　处：《中山大学学报（自然科学版）》2016年第2期23-27,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(11371248);安徽省高等学校省级自然科学研究资助项目(KJ2015A418)

摘　　要：研究了具有内部激波的非线性反应扩散方程奇摄动广义初始边值问题。在适当的条件下,讨论了退化问题的广义外部解并引入伸长变量,构造了原问题具有内部激波和初始层校正项的广义解的形式渐近展开式。最后,利用泛函分析不动点理论得到了原初始边值问题广义解的存在性和一致有效的内部激波广义渐近解。The nonlinear singular perturbation interior layer initial boundary value problem for the reaction diffusion equation is considered. Under suitable conditions,the reduced problem generalized outer solution is discussed. By introducing a stretched variable,the formal asymptotic expansion for the generalized solution with interior layer and initial layer corrective terms is constructed. Finally,using the fixed point theory of functional analysis,the existence and uniformly valid interior shock asymptotic solution for the original initial boundary value problems are proved.

关 键 词：非线性 激波 渐近解 

分 类 号：O175.29[理学—数学]