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Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. (English) Zbl 1027.80505

Summary: Using detailed asymptotic analyses of the dynamics of the phase-field model, we show that the major sharp-interface models (Stefan, modified Stefan, Hele-Shaw, etc.) all arise as limiting cases of the phase-field equations. The scaling of the physical parameters in the microscopics leads to distinct macroscopic models with critical differences.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
35Q60 PDEs in connection with optics and electromagnetic theory
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