摘要
研究了一类广义抛物型方程奇摄动问题.首先在一定的条件下,提出了一类具有两参数的非线性非局部广义抛物型方程初始-边值问题.其次证明了相应问题解的存在性.然后,通过Fredholm积分方程得到了初始-边值问题的外部解.再利用泛函分析理论和伸长变量及多重尺度法,分别构造了初始-边值问题广义解的边界层、初始层项,从而得到了问题的形式渐近展开式.最后利用不动点理论证明了对应的非线性非局部广义抛物型方程的奇异摄动初始-边值问题的广义解的渐近展开式的一致有效性.
A class of generalized parabolic equation singular perturbation problems were considered. Firstly,under suitable conditions,a class of nonlinear nonlocal generalized parabolic equation initial-boundary value problems with two parameters were raised. Secondly,the existence of solutions to corresponding problems was proved. Next,from the Fredholm integral equation,the outer solutions to the initial-boundary value problems were found,and the boundary and initial layer terms were structured by means of the theory of functional analysis,the stretched variables and the multiscale methods,respectively. Then the formal asymptotic expansion of the problem was obtained. Finally,according to the fixed point theorem,the uniform validity of the asymptotic expansion of generalized solutions to the corresponding nonlinear nonlocal initial-boundary value problems was proved.
出处
《应用数学和力学》
CSCD
北大核心
2017年第12期1405-1411,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11202106)
安徽省教育厅自然科学基金(KJ2015A347
KJ2017A702)
安徽省高校优秀青年人才支持计划重点项目(gxyqZ D2016520)~~
关键词
奇异摄动
渐近展开
一致有效性
singular perturbation
asymptotic expansion
uniform validity
