Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature
- 1 June 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in European Journal of Applied Mathematics
- Vol. 1 (2) , 101-111
- https://doi.org/10.1017/s0956792500000103
Abstract
The coupling of the Stefan equation for the heat flow with the Gibbs–Thomson law relating the melting temperature to the mean curvature of the phase interface is considered. Solutions, global in time, are constructed which satisfy the natural a priori estimates. Mathematically the main difficulty is to prove a certain regularity in time for the temperature and the indicator function of the phase separately. A capacity type estimate is used to give an L1 bound for fractional time derivatives.Keywords
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