Weak asymptotic solution of the phase field system in the case of confluence of free boundaries in the Stefan problem with undercooling

摘要

We assume that the Stefan problem with undercooling has a classical solutionuntil the moment of contact of free boundaries and the free boundaries havefinite velocities until the contact. Under these assumptions, we construct asmooth approximation of the global solution of the Stefan problem withundercooling, which, until the contact, gives the classical solution mentionedabove and, after the contact, gives a solution which is the solution of theheat conduction equation.