A modified Stefan problem as a limit of the asymptotics of a phase field system (Q1363871)
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scientific article; zbMATH DE number 1050592
| Language | Label | Description | Also known as |
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| English | A modified Stefan problem as a limit of the asymptotics of a phase field system |
scientific article; zbMATH DE number 1050592 |
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A modified Stefan problem as a limit of the asymptotics of a phase field system (English)
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20 August 1997
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A solution to the equations of a phase space that is asymptotic with respect to the parameter \(\varepsilon\ll 1\) is constructed. The evaluation of a uniform limit of this solution when \(\varepsilon\to 0\) results in a modified Stefan problem with the Gibbs-Thompson condition for temperature. The concepts elaborated in this paper are close to those of Oleinik's method of a vanishingly small viscosity, where the correct Hugoniot conditions for a discontinuous solution to the Hopf equation were obtained from an equation with small viscosity and subsequent passage to the limit.
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equations of a phase space
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modified Stefan problem
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Gibbs-Thompson condition
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