一类燃烧问题的奇摄动解

一类燃烧问题的奇摄动解 A Singularly Perturbed Solution for a Class of Burning Problem 许永红 XU Yonghong1 1 first-author 林万涛 LIN Wantao2 2 温朝晖 WEN Zhaohui3 3 莫嘉琪 MO Jiaqi4 4 蚌埠学院数理系 蚌埠学院数理系 Department of Mathematics and Physics,Bengbu College Department of Mathematics and Physics,Bengbu College 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamic,Institute of Atmospheric Physics,Chinese Academy of Sciences State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamic,Institute of Atmospheric Physics,Chinese Academy of Sciences 安徽财经大学统计与应用数学学院 安徽财经大学统计与应用数学学院 School of Statistics and Applied Mathematics,Anhui University of Finance and Economics School of Statistics and Applied Mathematics,Anhui University of Finance and Economics 安徽师范大学数学系 安徽师范大学数学系 Department of Mathematics,Anhui Normal University Department of Mathematics,Anhui Normal University 讨论了一类燃烧问题.利用奇摄动方法构造了问题解的边界层和内层.指出了相应问题存在内部冲击波,并得到了解的渐近展开式.最后通过一个具体例子描述了问题解出现的火焰冲击波的性态. A class of combustion problem is considered.Using the singular perturbation method,the boundary and the interior layers of solution for the problem are constructed.And we pointed out that there is a kind of interior shock wave and then the asymptotic expansion of solution is obtained.Finally,the behavior of the flame shock wave is described using the specific example. 奇摄动 燃烧问题 渐近解 singular perturbation reaction diffusion differential inequality 10.14188/j.1671-8836.2013.03.018 O411.1 国家自然科学基金（41275062,41175058）;中国科学院战略性先导科技专项（XDA01020304）;安徽教育厅自然科学基金（KJ2012Z245,KJ2012A001,1208085QA11,KJ2013B003）资助项目 2013-03-01 2021-04-01 3 59