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Spherically symmetric Stefan problem with the Gibbs–Thomson law at the moving boundary

Published online by Cambridge University Press:  26 September 2008

I. G. Götz  and
M. Primicerio
I. G. Götz
Affiliation:
Institute of Applied Mathematics and Statistics, Technical University of Munich, Dachauer Str. 9a, 80335 Munich, Germany
M. Primicerio
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Universita di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
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Abstract

This paper deals with the spherically symmetric Stefan problem in three space dimensions. The melting temperature satisfies the Gibbs–Thomson law. The solution is obtained as a limit of solutions of similar problems containing a small additional kinetic term in the melting temperature. Under some structural assumptions we show that the phase-change boundary has at most one discontinuity point t = T0 (see the corresponding result for the planar Stefan problem in Götz & Zaltzman (1995)). In the one-phase problem the discontinuity point always exists. At the time T0 the whole solid phase melts instantaneously. We study also the asymptotical stability (t → ∞) of stationary solutions satisfying boundary conditions of thermostat type.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 3 , June 1996 , pp. 249 - 275
Copyright
Copyright © Cambridge University Press 1996

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