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

2005/12/27 by В. Г. Данилов, Danilov, V. G.
Computer Science · Materials Science · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.math-ph/0512086

openalex publication_date 2005/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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