Sakiadis流动的一致有效级数解

A Uniformly Valid Series Solution to Sakiadis Flow

通过引入一个变换式,克服了Sakiadis流动中半无限大流动区域以及无穷远处渐近边界条件所带来的数学处理上的困难.基于泛函分析中的不动点理论,采用不动点方法求解了变换后的非线性微分方程,获得了Sakiadis流动的近似解析解.该近似解析解用级数的形式来表达并在整个半无限大流动区域内一致有效.

In order to overcome the major mathematical difficulties in Sakiadis flow due to the semi-infinite flow domain and the asymptotic far field boundary condition,transformations were introduced for both the related independent variables and functions simultaneously,to convert the semi-infinite domain to a finite one and the asymptotic boundary condition to a convenient form. Then,based on the fixed point theory in functional analysis,the deduced nonlinear differential equation was solved,and an approximate semi-analytical series solution to Sakiadis flow was obtained. The calculation results show that the solution is uniformly valid in the semi-infinite domain,and the fixed point method makes an effective way to achieve approximate analytical solutions to differential equations.