This paper provides a new proof of the existence and uniqueness of the solution for a nonlinear boundary value problem

$$\left\{\begin{array}{rl}{\left[(1+\delta y)y^{\prime }\right]}^{\prime }+2x(1+\gamma y)y^{\prime }& =0,0<x<\infty ,\\ y(0)=0,y(\infty )& =1,\end{array}\right.$$

which describes the study of two-phase Stefan problems on the semi-infinite line [0, ∞). This result considerably extends the analysis of a recent work. A highly accurate analytic approximate solution of this problem is also provided via the Adomian decomposition method.

中文翻译：

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两相Stefan问题中修正误差函数的存在唯一性及解析近似解

本文为非线性边值问题解的存在唯一性提供了新的证明

$$\left\{\begin{array}{rl}{\left[(1+\delta 是){是}^{\prime }\right]}^{\prime }+2X(1+\gamma 是){是}^{\prime }& =0,0<X<\infty ,\\ 是(0)=0,是(\infty )& =1,\end{array}\right.$$

它描述了半无限线 [0, ∞ )上两相 Stefan 问题的研究 。这一结果大大扩展了对最近工作的分析。还通过 Adomian 分解方法提供了该问题的高精度解析近似解。