| 一类带小扰动的Raman散射的数学模型研究 |
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| 引用本文： | 肖蕊梅,江新华,李明远.一类带小扰动的Raman散射的数学模型研究[J].北京化工大学学报(自然科学版),2021,48(5):124-128. |
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| 作者姓名： | 肖蕊梅 江新华 李明远 |
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| 作者单位： | 北京化工大学 数理学院, 北京 100029 |
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| 摘 要： | 研究一类带小扰动的Raman散射的数学模型的相关问题，使用积分方程和Banach不动点定理证明初值问题的解的存在唯一，并利用多重尺度法求解渐近解，再借助积分方程和Gronwall不等式得到渐近解的余项估计，从而证明了渐近解的一致有效性。
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| 关 键 词： | Raman散射 摄动方法 渐近解 余项估计 |
| 收稿时间： | 2020-05-14 |
A mathematical model of Raman scattering with small perturbations |
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| XIAO RuiMei,JIANG XinHua,LI MingYuan.A mathematical model of Raman scattering with small perturbations[J].Journal of Beijing University of Chemical Technology,2021,48(5):124-128. |
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| Authors: | XIAO RuiMei JIANG XinHua LI MingYuan |
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| Affiliation: | College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | In this paper, we study a mathematical model of Raman scattering with small perturbations. Using an integral equation and the Banach fixed point theorem, the existence and the uniqueness of the solution for the initial value problems is proved. The first term of the asymptotic solution is obtained by using the method of multiple scale. With the use of the integral equation and Gronwall's inequality, the error estimation of the asymptotic solution is shown to be uniformly valid. |
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| Keywords: | Raman scattering perturbation methods asymptotic solution error estimation |
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