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 引用本文: 史娟荣, 莫嘉琪. 一类奇异摄动燃烧模型的渐近解[J]. 应用数学和力学, 2016, 37(7): 691-698.
SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293
 Citation: SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698.

一类奇异摄动燃烧模型的渐近解

doi: 10.21656/1000-0887.360293

作者简介:史娟荣(1981—),女，副教授,硕士（E-mail: ahjdshjr@126.com）;莫嘉琪(1937—)，男，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).
• 中图分类号: O175.14

Asymptotic Solutions to a Class of Singular Perturbation Burning Models

Funds: The National Natural Science Foundation of China(41275062;11202106)
• 摘要: 讨论了一类具有两参数的非线性奇异摄动的燃烧模型.首先，利用摄动方法, 得到了燃烧模型的外部解；其次，引入一个伸长变量, 构造了燃烧模型解的初始层的校正项; 然后, 利用多重尺度方法和合成展开方法构造了模型解的边界层校正项, 并由此得到了原初始边值问题的渐近解；最后,利用微分不等式相关的理论证明了所得到的渐近解的一致有效性.用该文的求解方法简单而可行.
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出版历程
• 收稿日期:  2015-10-27
• 修回日期:  2015-11-27
• 刊出日期:  2016-07-15

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