*Mathematical Methods in the Applied Sciences*On the Stefan Problem With Nonlinear Thermal Conductivity

The solution is obtained and validated by an existence and uniqueness
theorem for the following nonlinear boundary value problem
\[
\frac{d}{dx}(1+\delta
y+\gamma
y^{2})^{n}\frac{dy}{dx}]+2x\frac{dy}{dx}=0,\,\,\,x>0,\,\,y(0)=0,\,\,\,y(\infty)=1,
\] which was proposed in 1974 by [1] to represent a
Stefan problem with a nonlinear temperature-dependent thermal
conductivity on the semi-infinite line (0;1). The modified error
function of two parameters
$\varphi_{\delta,\gamma}$
is introduced to represent the solution of the problem above, and some
properties of the function are established. This generalizes the results
obtained in [3, 4].

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