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中文摘要：
研究了一类大气非线性尘埃等离子体扩散方程初值问题．首先在无扰动情形下，利用Foutier变换方法得到了尘埃等离子体扩散方程初值问题的精确解，接着引入一个同伦映射．并选取初始近似函数，再用同伦映射理论，依次求出非线性尘埃等离子体扰动初值问题的各次近似解析解．引用不动点理论，指出了近似解析解的有效性和各次近似解的近似度，用模拟曲线和表格给出近似对照例子．最后，简述了用同伦映射方法得到的近似解的物理意义．指出了用上述方法得到的各次近似解具有便于求解、精度高等优点．
英文摘要：
A class of nonlinear diffusion equation initial value problems about dust plasma diffu- sion in atmosphere were investigated. Firstly, the exact solution to the non-disturbed dust plasma diffusion equation was obtained with the Fourier transformation method. Then a homotopic mapping was introduced and an initial approximate function was chosen to fred out successively the arbitrary-order approximate analytic solutions to the disturbed initial value problems according to the homotopic mapping theory again. Next, the fixed point theory was applied to make clear validity of the approximate analytic solutions and determine their respective degrees of approximation. In the 2 examples, simulation curves and tables were given to make comparison between the exact solution and the various-order approximate ones. Finally, the physical sense of the approximate solutions obtained with the homotopic mapping method was analyzed simply and their easy application and high accuracy were examined.
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