| 非线性波动系统的冲击层解 |
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| 引用本文： | 陈怀军,徐建中,莫嘉琪.非线性波动系统的冲击层解[J].吉林大学学报(理学版),2019,57(3):493-499. |
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| 作者姓名： | 陈怀军 徐建中 莫嘉琪 |
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| 作者单位： | 安徽师范大学 数学与统计学院,安徽 芜湖,241003;亳州学院 电子与信息工程系,安徽 亳州,236800 |
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| 基金项目： | 国家自然科学基金;安徽省高等学校自然科学研究重点项目;安徽省高等学校优秀青年人才支持计划;安徽省优秀教学团队基金;安徽省优秀教学团队基金 |
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| 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.
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| 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 |
| 收稿时间： | 2018-07-02 |
Shock Layer Solution of Nonlinear Wave System |
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| CHEN Huaijun,XU Jianzhong,MO Jiaqi.Shock Layer Solution of Nonlinear Wave System[J].Journal of Jilin University: Sci Ed,2019,57(3):493-499. |
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| Authors: | CHEN Huaijun XU Jianzhong MO Jiaqi |
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| Institution: | 1. School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003, Anhui Province, China;2. Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, Anhui Province, China
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| Abstract: | 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. |
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| Keywords: | nonlinear wave third boundary value problem outer solution correction term singular perturbation asymptotic shock wave
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