Classical solutions to parabolic systems with free boundary of Stefan type

Abstract

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 modification of the standard change of variables method and coercive estimates in a weighted Hölder space (the weight being a power of $t$) we obtain solutions with maximal global regularity (having at least equal regularity for $t>0$ as at the initial moment).