Advances in Differential Equations
- Adv. Differential Equations
- Volume 10, Number 12 (2005), 1345-1388.
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 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).
Adv. Differential Equations Volume 10, Number 12 (2005), 1345-1388.
First available in Project Euclid: 18 December 2012
Permanent link to this document
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. https://projecteuclid.org/euclid.ade/1355867738.