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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (6): 663-672.doi: 10.3969/j.issn.1005-3085.2018.06.006

• • 上一篇    下一篇

大气尘埃等离子体扩散问题奇异摄动解

汪维刚1,   莫嘉琪2   

  1. 1- 合肥幼儿师范高等专科学校基础部，合肥  230011
    2- 安徽师范大学数学与统计学院，芜湖  241003
  • 收稿日期:2017-08-01 接受日期:2018-01-09 出版日期:2018-12-15 发布日期:2019-02-15
  • 基金资助:
    国家自然科学基金(41275062)；安徽省教育科学规划课题(JG10068)；安徽省教育厅自然科学重点基金项目(KJ2018A0964; KJ2017A901).

The Singular Perturbation Solution to Dust Plasma Diffusion Problem in Atmosphere

WANG Wei-gang1,   MO Jia-qi2   

  1. 1- Department of Basics, Hefei Preschool Education College, Hefei 230011
    2- School of Mathematics & Statistics, Anhui Normal University, Wuhu 241003
  • Received:2017-08-01 Accepted:2018-01-09 Online:2018-12-15 Published:2019-02-15
  • Supported by:
    The National Natural Science Foundation of China (41275062); the Key Natural Science Foundation of the Education Department of Anhui Province (KJ2018A0964; KJ2017A901); the Education Science Programming Foundation of Anhui Province (JG10068).

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摘要： 为了有效地控制尘埃颗粒物的污染、改善环境与空气质量，有必要掌握大气尘埃 颗粒物的分布．本文研究一类大气非线性等离子体扩散方程初值问题．首先利用奇异摄动和Fourier变换方法，分别求出了问题的外部解和初始层校正项，并构造了解的形式渐近展开式．其次利用先验估计证明了解的展开式的一致有效性．然后举例给出了各次渐近近似解．最后叙述了近似解析解的物理意义．通过近似函数可定量地计算出尘埃等离子体相关的物理量，以采取适当的措施，有助于减少灾害的影响．

关键词: 大气, 扩散方程, 等离子体, 奇异摄动, Fourier变换

Abstract: In order to efficiently control polluted air of dust particles and to improve the quality of ambient air, it is necessary to examine the distribution of the dust particles. In this paper, we consider a class of nonlinear diffusion equation initial value problem for the dust plasma diffusion equation in atmosphere. Firstly, the outer and initial corrective layer terms are obtained respectively by using the singular perturbation method and Fourier transformation. And the formally asymptotic expansion of solution is constructed. Secondly, using the prior estimate theory, the uniformly validity for expansion is proved. Then the any orders of asymptotic approximate solutions are derived. Finally, the physical meaning of the approximate analytic solution is investigated. From the approximate function, we can compute the correlative physical quantity of dust plasma, which can help us to adopt appropriate measures and to reduce the impact of disaster.

Key words: atmosphere, diffusion equation, plasma, singular perturbation, Fourier transformation

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