关于Boussinesq方程Barenblatt幂级数解的注记

通过幂级数展开的方法推求得出了Barenblatt幂级数解的各项系数之间的递推公式(对半无限长多孔介质中地下水流动的Boussinesq方程的自相似解，在边界水头随时间幂函数变化的条件下，Barenblatt（1952）得到了一个幂级数解，但他仅仅列出了其前3项的系数，既没有给出整个幂级数解所有系数的递推关系式，也没有证明该幂级数解的收敛性．),并对该级数的收敛性进行了证明，同时对解的实际应用作了讨论．这些研究结论易于理解，方便工程技术人员应用于流域水文学和基流研究及解决农业排水等实际问题．

Note on the Barenblatt Power Series Solution to the Boussinesq Equation

A self-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium when the hydraulic head at the boundary behaves like a power of time was presented(Barenblatt(1952) obtained a power series solution,but he listed only the first three coefficients and did not give the recurrent formula among the coefficients.A formal proof of convergence of the series did not appear).The recurrent formula for the coefficients was obtained using the method of power series expansion,and the convergence of the series was proven.The results can be easily understood and used by engineers in catchment hydrology and baseflow studies as well as agricultural drainage problems.