非线性波动系统的冲击层解  

Shock Layer Solution of Nonlinear Wave System

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

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

出　　处：《吉林大学学报（理学版）》2019年第3期493-499,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:41275062);安徽省高校自然科学研究重点项目(批准号:KJ2017A704);安徽省高校优秀青年人才支持计划项目(批准号:gxyq2018116);安徽省优秀教学团队基金(批准号:2016jytd080;2015jytd048)

摘　　要：考虑非线性奇异摄动波动方程第三边值问题,先利用奇异摄动法构造外部解,再引入伸长变量依次得到解的冲击波尖层、初始层及边界层的校正项,最后给出问题解的渐近展开式,并证明渐近解的一致有效性.We considered the third boundary value problem of nonlinear singularly perturbed wave equation. Firstly, the outer solution was constructed by using singular perturbation method. Secondly, correction terms of the shock layer, initial layer and boundary layer were obtained by using the stretched variables. Finally, the asymptotic expansion of solution to problem was given , and the uniform validity of its asymptotic solution was proved.

关 键 词：非线性波动 第三边值问题 外部解 校正项 奇摄动 渐近 冲击波 

分 类 号：O175.29[理学—数学]