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The macroscopic description of matter undergoing a phase change (the Stefan Problem) can be formulated as a set of coupled, non-linear partial differential equations. For the case of one space dimension, the thesis develops three approximation methods to solve these equations. (a) Asymptotic Expansions With the Green's functions to suit the given boundary conditions, the system can be transformed into a set of integral equations. For the case where the initial phase grows without limit as т → ∞doi:10.14288/1.0080116 fatcat:xl4xqvexlvayzmy72wcwegblwu