一类弱非线性临界奇摄动积分边界问题  

A Class of Weakly Nonlinear Critical Singularly Perturbed Integral Boundary Problems

作　　者：张浩 汪娜 Zhang Hao;Wang Na(College of Sciences,Shanghai Institute of Technology,Shanghai 201418)

机构地区：[1]上海应用技术大学理学院,上海201418

出　　处：《数学物理学报（A辑）》2022年第4期1060-1073,共14页Acta Mathematica Scientia

基　　金：上海应用技术大学自然科学项目(1021GK210006141)。

摘　　要：基于边界层函数法,研究了一类弱非线性临界情况下的带有积分边界条件的奇异摄动问题.在该文的框架下,作者不仅构造了原方程解的渐近展开式,还给出了一致有效渐近展开式的证明.同时,该文给出了一个例子来说明文中的结果,并且画出了近似解与精确解在不同小参数下比较的图像.Based on the boundary layer function method,a class of singularly perturbed problems with integral boundary conditions in weakly nonlinear critical cases are studied.In the framework of this paper,we not only construct the asymptotic expansion of the solution of the original equation,but also prove the uniformly effective asymptotic expansion.At the same time,we give an example to illustrate our results,The comparison images of approximate solution and exact solution under different small parameters are drawn.

关 键 词：临界情况 奇异摄动 边界层函数法 近似解 

分 类 号：O175.14[理学—数学]