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.


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