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

Published online by Cambridge University Press:  01 October 2007

V. G. DANILOV
V. G. DANILOV*
Affiliation:
Moscow Technical University of Communication and Informatics email: danilov@miem.edu.ru
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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.

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Papers
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European Journal of Applied Mathematics , Volume 18 , Issue 5 , October 2007 , pp. 537 - 569
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Copyright © Cambridge University Press 2007

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