The classical Stefan problem proffers a suitable model for determining the temperature regimes as well as conjugate interfacial positions for multiphase problems. Obtaining the solutions to these problems exactly, especially in systems with cylindrical or spherical symmetry, is often an arduous task. This is largely due to inherent nonlinearities in the mathematical statements of Stefan problems.

In this paper, a tractable and effective approach is proposed. Subsequent to a recast as a system of differential-difference equations, and a methodical reduction to constant coefficient difference equations, exact similarity solutions are derived for a class of heterogeneous two-phase Stefan problems with cylindrical or spherical symmetry in one spatial dimension, under either Gaussian or hypergeometric perturbations.

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