吉林大学学报（理学版）2017，Vol.55Issue(5)：1055-1060,6.DOI:10.13413/j.cnki.jdxblxb.2017.05.02
一类广义奇摄动非线性双曲型积分-微分方程模型
A Class of Generalized Nonlinear Hyperbolic Integral-Differential Equation with Singular Perturbation Model
摘要
Abstract
We considered a class of generalized two parameter nonlinear hyperbolic integral-differential equation with singular perturbation model.Firstly,the generalized outer solution of the model was obtained by using the generalized Fredholm type integral equation.Secondly,the boundary layer corrective term of the generalized solution was obtained by using the method of multiple scale variables.Thirdly,the initial layer corrective term of the generalized solution was obtained by using the stretched variable method.Finally,the synthetic asymptotic expansion of the generalized singular perturbation solution was constructed,and the uniform validity of the asymptotic expansion of the solution was proved by using the fixed point theory.关键词
积分-微分方程/奇摄动/双曲型方程Key words
integral-differential equation/singular perturbation/hyperbolic equation分类
数理科学引用本文复制引用
冯依虎,莫嘉琪..一类广义奇摄动非线性双曲型积分-微分方程模型[J].吉林大学学报（理学版）,2017,55(5):1055-1060,6.基金项目
国家自然科学基金(批准号:11202106)、安徽省教育厅自然科学重点项目基金(批准号:KJ2015A347 （批准号:11202106）
KJ2017A702)和安徽省高校优秀青年人才支持计划重点项目(批准号:gxyqZD2016520). （批准号:gxyqZD2016520）
