In this article we study supercooling from a macroscopic point of view by m
odeling the evolution of a supercooled body from its liquid state to its so
lid state. A first model, which would be expected to have discontinuous sol
utions, is regularized by introducing an intrinsic viscous dissipation. By
applying the classical method of Faedo-Galerkin, this regularized model is
shown to have a global smooth solution, which describes the state transitio
n of the supercooled body approximately. (C) 2001 Academic Press.