一类催化反应Robin问题的渐近解  

Asymptotic Solutions to a Class of Catalytic Reaction Robin Problems

作　　者：徐建中 莫嘉琪 XU Jianzhong;MO Jiaqi(Department of Electronics and Information Engineering,Bozhou University,Bozhou,Anhui 236800,P.R.China;School of Mathematics&Statistics,Anhui Normal University,Wuhu,Anhui 241003,P.R.China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《应用数学和力学》2020年第1期107-114,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11771005);安徽省教育厅自然科学重点基金(KJ2019A1303);安徽省高校优秀青年人才支持计划(gxyq2018116)~~

摘　　要：研究了一类非线性催化反应微分方程Robin问题.在一定的条件下,先利用摄动方法求出了原Robin问题的外部解,然后用伸长变量和幂级数理论分别构造了解的第一和第二边界层校正项,从而得到了Robin问题解的形式渐近展开式.最后利用微分不等式理论,证明了问题解的渐近表示式的一致有效性.A class of Robin problems of nonlinear catalytic reaction differential equations were studied.Firstly,under the suitable conditions,the outer solution to the original Robin problem was obtained with the perturbation method.Then by means of the stretched variable and the power series,the 1st and 2nd boundary layer corrective terms were constructed respectively,and the formal asymptotic expansion was structured.Finally,based on the theory of differential inequalities the formal asymptotic expression of the solution to the Robin problem was given.Finally,the uniform validity of the asymptotic expression of the solution to problem was proved.

关 键 词：催化反应 ROBIN问题 奇异摄动 

分 类 号：O175.14[理学—数学]