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Mathematical analysis of phase-field equations with numerically efficient coupling terms. (English) Zbl 0986.35116
Summary: 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.

MSC:
35Q72 Other PDE from mechanics (MSC2000)
35R35 Free boundary problems for PDEs
74N05 Crystals in solids
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