In this note I review some results achieved from a collaboration with Jürgen Sprekels and concerning the asymptotic behaviour of initial-boundary value problems for the Penrose-Fife phase-field model as the coefficients of the differential terms for the order parameter tend to zero. In the limit procedure one gets either standard or relaxed Stefan problems, still with heat flux proportional to the gradient of the inverse absolute temperature. After focusing on the problems relaxed in time and recalling the convergence results, we add a small new contribution by proving an error estimate.
Error estimates for nonlinear Stefan problems obtained as asymptotic limits of a Penrose-Fife model
Colli P.
1996-01-01
Abstract
In this note I review some results achieved from a collaboration with Jürgen Sprekels and concerning the asymptotic behaviour of initial-boundary value problems for the Penrose-Fife phase-field model as the coefficients of the differential terms for the order parameter tend to zero. In the limit procedure one gets either standard or relaxed Stefan problems, still with heat flux proportional to the gradient of the inverse absolute temperature. After focusing on the problems relaxed in time and recalling the convergence results, we add a small new contribution by proving an error estimate.File in questo prodotto:
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