双参数奇摄动非线性抛物型系统的广义尖层解

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双参数奇摄动非线性抛物型系统的广义尖层解冯依虎^1,2, 侯磊², 莫嘉琪³1. 亳州学院电子与信息工程系, 亳州 236800;
2. 上海大学数学系, 上海 200436;
3. 安徽师范大学数学与统计学院, 芜湖 241003 The Generalized Spike Layer Solution to Singular Perturbation Nonlinear Parabolic System with Two Parameters FENG Yihu^1,2, HOU Lei², MO Jiaqi³1. Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, China;
2. Department of mathematics, Shanghai University, Shanghai 200436, China;
3. School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003, China

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摘要本文研究了一类非线性抛物型微分系统的奇异摄动问题.首先利用奇异摄动方法构造了外部解.其次，分别采用多尺度法和伸长变量法获得尖层校正项、边界层校正项和初始层校正项.最后得到了广义解的渐近展开解.利用不动点定理证明了渐近解的一致有效性.该渐近解可用于对广义解进行解析运算，可以了解其更多的特征，因此具有较好的应用前景.

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收稿日期: 2019-04-16

PACS:

O175.4

基金资助:国家自然科学基金（11271247），安徽省高校优秀青年人才支持计划重点项目（gxyqZD2016520），安徽省教育厅自然科学重点基金项目（KJ2015A347，KJ2017A702，KJ2019A1300），安徽省教育厅重点教研项目（2018jyxm0594，2016jyxm0677，2017jyxm0591），亳州学院重点教学研究项目（2017zdjy02）和亳州学院重点科学研究项目（BYZ2017B02，BYZ2017B03）资助.

引用本文:

冯依虎, 侯磊, 莫嘉琪. 双参数奇摄动非线性抛物型系统的广义尖层解[J]. 应用数学学报, 2020, 43(5): 821-832. FENG Yihu, HOU Lei, MO Jiaqi. The Generalized Spike Layer Solution to Singular Perturbation Nonlinear Parabolic System with Two Parameters. Acta Mathematicae Applicatae Sinica, 2020, 43(5): 821-832.

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