Advances in Differential Equations

Classical solutions to parabolic systems with free boundary of Stefan type

G. I. Bizhanova and J. F. Rodrigues

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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).

Article information

Adv. Differential Equations, Volume 10, Number 12 (2005), 1345-1388.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35B65: Smoothness and regularity of solutions 35K55: Nonlinear parabolic equations 35K60: Nonlinear initial value problems for linear parabolic equations 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Bizhanova, G. I.; Rodrigues, J. F. Classical solutions to parabolic systems with free boundary of Stefan type. Adv. Differential Equations 10 (2005), no. 12, 1345--1388.

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