大气尘埃等离子体扩散问题奇异摄动解  

The Singular Perturbation Solution to Dust Plasma Diffusion Problem in Atmosphere

作　　者：汪维刚 莫嘉琪 WANG Wei-gang;MO Jia-qi(Department of Basics,Hefei Preschool Education College,Hefei 230011;School of Mathematics&Statistics,Anhui Normal University,Wuhu 241003)

机构地区：[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

出　　处：《工程数学学报》2018年第6期663-672,共10页Chinese Journal of Engineering Mathematics

基　　金：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)~~

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.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.

关 键 词：大气 扩散方程 等离子体 奇异摄动 FOURIER变换 

分 类 号：O175.29[理学—数学]