Singular limit of a transmission problem for the parabolic phase-field model.
Two standard phase-field systems with different physical parameters are considered in two adjacent domains with transmission conditions on the fixed common boundary, as a model for solid-liquid phase transitions in two different substances with heat exchange across the interface. The author proves the existence of a weak solution in the case of positive phase relaxation coefficients. If one of these coefficients tends to zero, it is shown that the corresponding solutions converge to the unique weak solution of the limit system.
scientific article; zbMATH DE number 1516992
scientific article