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两参数非线性发展方程的奇摄动尖层解
欧阳成¹, 陈贤峰², 莫嘉琪³
1.湖州师范学院理学院, 浙江湖州 313000;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

摘要:

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度，构造了初始边值问题外部解和尖层、边界层和初始层校正项，得到了问题形式解.利用不动点定理，证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.

关键词: 尖层奇摄动发展方程

DOI：

分类号:O175.4

基金项目:Supported by the National Natural Science Foundation of China (11371248) and the Natural Science Foundation of Zhejiang Province, China (LY13A010005).

THE POINTED LAYER SOLUTION OF SINGULAR PERTURBATION FOR NONLINEAR EVOLUTION EQUATIONS WITH TWO PARAMETERS

OUYANG Cheng¹, CHEN Xian-feng², MO Jia-qi³

1.Faculty of Science, Huzhou University, Huzhou 313000, China;2.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China;3.Department of Mathematic, Anhui Normal University, Wuhu 241003, China

Abstract:

In this paper,the nonlinear singular perturbation problem for the evolution equations is studied.The outer solution and corrective terms of the pointed,boundary and initial layers for the solution are constructed.By using the fixed point theorem,the uniformly validity of solution to the problem ia proved and the results of the study for the singular perturbation with two parameters is extended.

Key words: pointed layer singular perturbation evolution equation