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Classical solutions to parabolic systems with free boundary of Stefan type

Motivated by the classical model for the binary alloy solidification (crystallization) problem, we show the local in time existence and uniqueness of solutions to a parabolic system strongly coupled through free boundary conditions of Stefan type. Using a modi¯cation of the standard change of variables method and coercive estimates in a weighted HÄolder space (the weight being a power of t) we obtain solutions ...