Abstract
It is well known that the classical description of melting/solidification processes leads to a mathematical problem in which the regions occupied by the two phases are separated by a sharp interface, the free boundary. On such an interface the temperature u is set equal to the phase-change temperature (which is assumed constant, say 0) whereas in the solid and in the liquid regions u is negative or positive respectively and satisfies the corresponding heat conduction equation; the energy balance (Stefan condition) across the free boundary completes the model along with initial and boundary conditions.
Work partially supported by the Italian CNR Strategic Project “Applicazioni industiali e technologiche della matematica” and by the Italian National Project “Equazioni di evoluzione e applicazioni fisico-matematiche”.
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© 1989 Birkhäuser Verlag, Basel
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Fasano, A., Primicerio, M. (1989). Phase Change Without Sharp Interfaces. In: Rodrigues, J.F. (eds) Mathematical Models for Phase Change Problems. International Series of Numerical Mathematics, vol 88. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9148-6_7
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DOI: https://doi.org/10.1007/978-3-0348-9148-6_7
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