Confluence of the nonlinear waves in the Stefan problem with undercooling

2006/12/22 by V. G. Danilov, Danilov, V. G., V. Yu. Rudnev +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0612713

36 pages, Latex

arxiv created 2006/12/22 · arxiv updated 2009/12/01

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 continuous velocities until the moment of 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 equation.

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