Geodesic
Mathematical analysis of phase-field equations with numerically efficient coupling terms
Michal Beneš1
1Charles University, Praha, Czech Republic
Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 201-212

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This paper deals with the equations in a phase-field model with special terms coupling the heat equation and the equation of phase. A finer control of latent heat release together with a gradient coupling term in the phase equation are introduced as a consequence of an extensive numerical work with models of phase transitions within the context of the solidification of crystalline substances. We present a proof of the existence and uniqueness of the weak solution of the modified system of equations. Furthermore, we perform an asymptotic procedure to recover sharp-interface relations. Finally, several numerical studies demonstrate how the model behaves compared to its standard version.
DOI : 10.4171/ifb/38
Classification : 46-XX, 60-XX
Mots-clés : Phase field, microstructure growth, Stefan problem, compactness method

Michal Beneš  1

1 Charles University, Praha, Czech Republic 
Michal Beneš. Mathematical analysis of phase-field equations with numerically efficient coupling terms. Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 201-212. doi: 10.4171/ifb/38
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     title = {Mathematical analysis of phase-field equations with numerically efficient coupling terms},
     journal = {Interfaces and free boundaries},
     pages = {201--212},
     year = {2001},
     volume = {3},
     number = {2},
     doi = {10.4171/ifb/38},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/38/}
}
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