一类双参数非线性高阶反应扩散方程的摄动解法  

Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters

作　　者：汪维刚 许永红[2] 石兰芳[3] 莫嘉琪[4] 

机构地区：[1]安庆师范学院桐城教学部,安徽桐城231402 [2]蚌埠学院数学与物理系,安徽蚌埠233030 [3]南京信息工程大学数学与统计学院,南京210044 [4]安徽师范大学数学系,安徽芜湖241000

出　　处：《应用数学和力学》2014年第12期1383-1391,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202106);安徽省高等学校省级自然科学研究项目(KJ2013A133;KJ2014A151);江苏省自然科学基金(13KJB170016)~~

摘　　要：研究了一类两参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.首先,构造问题的外部解;之后在区域的边界邻域构造局部坐标系,再在该邻域中引入多尺度变量,得到问题解的边界层校正项;然后引入伸长变量,构造初始层校正项,并得到问题解的形式渐近展开式;最后建立了微分不等式理论,并由此证明了问题的解的一致有效的渐近展开式.用上述方法得到的各次近似解,具有便于求解、精度高等特点.The model for a class of high-order nonlinear reaction diffusion singularly perturbed problems with double parameters was addressed. With the singular perturbation method, the structure of the solution to the problem was discussed in the cases of double related small pa- rameters. Firstly, the outer solution to the boundary value problem was given. Secondly, the variable of multiple scales was introduced to obtain the boundary layer correction term for the solution. Then the stretched variable was applied to the boundary neighborhood to get the initial layer correction term. Finally, the theorem of differential inequalities was constructed and the uniformly valid asymptotic expansion of the solution to the problem was proved. The proposed method possesses the advantages of convenient use and high accuracy.

关 键 词：非线性 两参数 反应扩散 

分 类 号：O175.29[理学—数学]