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Behaviour of mushy regions under the action of a volumetric heat source
Author(s) -
Andreucci Daniele
Publication year - 1993
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670160104
Subject(s) - stefan problem , mathematics , action (physics) , phase change , energy (signal processing) , boundary (topology) , phase (matter) , heat equation , mathematical analysis , thermodynamics , mechanics , physics , statistics , quantum mechanics
In this paper we consider solutions to Stefan problems in spatial dimensions N ⩾ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.