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This paper considers a class of one-dimensional solidification problems, in which a kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with linear kinetic law is considered. This study indicates that the presence of a kinetic term at the interface can prevent finite-time blowup even though supercooling (superheating) exists. The mathematical erects of the kinetic term are discussed.
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A 1990 study studied this question.
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