One-Phase Spherical Stefan Problem with Temperature Dependent Coefficients

Abstract

The one-phase spherical Stefan problem with coefficients depending on the temperature is considered. The method of solving is based on the similarity principle, which enables us to reduce this problem to a nonlinear ordinary differential equation, and then to an equivalent nonlinear integral equation of the Volterra type. It is shown that the obtained integral operator is a contraction operator and a unique solution exists.