| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 303, n. 2, p. 669-687, MAR 15 2005. |
| Web of Science Citations: | 10 |
| Abstract | |
The article analyzes a two-dimensional phase-field model for a non-stationary process of solidification of a binary alloy with thermal properties. The model allows the occurrence of fluid flow in non-solid regions, which are a priori unknown, and is thus associated to a free boundary value problem for a highly non-linear system of partial differential equations. These equations are the phase-field equation, the heat equation, the concentration equation and a modified Navier-Stokes equations obtained by the addition of a penalization term of Carman-Kozeny type which accounts for the mushy effects. A proof of existence of weak solutions for such system is given. The problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder fixed point theorem. A solution is then found by using compactness argument. (C) 2004 Elsevier Inc. All fights reserved. (AU) | |