European Journal of Applied Mathematics

Papers

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

V. G. DANILOVa1

a1 Moscow Technical University of Communication and Informatics email: danilov@miem.edu.ru

Abstract

We assume that the Stefan problem with underheating has a classical solution until the moment of contact of two distinct free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we construct a smooth approximation of the global solution of the Stefan problem with underheating, which, until the contact, gives the classical solution mentioned above and, after the contact, gives a solution that is the solution of the heat equation.

(Received June 20 2006)

(Revised March 21 2007)

(Online publication August 21 2007)