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