A mathematical one-dimensional model of supercooling solidification (Q1090868)

A model for one-dimensional solidification is discussed that takes supercooling effects into account. In particular, it is assumed that the rate of solidification is proportional to the difference \(\Delta\) F of the free energies in the liquid and the solid phase, respectively. Since \(\Delta\) F is proportional to the difference between the equilibrium temperature and the actual temperature, solidification under supercooling is favoured. For the corresponding model, the existence of a solution is proved. It is unique provided the initial supercooling is small. A convergent difference scheme for the numerical approximation of the solution is introduced.