| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, ICMC, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 13, n. 2, p. 429-450, JUL 2005. |
| Web of Science Citations: | 7 |
| Abstract | |
We consider a tridimensional phase-field model for a solidification/melting non-stationary process, which incorporates the physics of binary alloys, thermal properties and fluid motion of non-solidified material. The model is a free-boundary value problem consisting of a highly non-linear parabolic system including a phase-field equation, a heat equation, a concentration equation and a variant of the Navier-Stokes equations modified by a penalization term of Carman-Kozeny type to model the flow in mushy regions and a Boussinesq type term to take into account the effects of the differences in temperature and concentration in the flow. A proof of existence of generalized solutions for the system is given. For this, the problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder's fixed point theorem. A solution of the original problem is then found by using compactness arguments. (AU) | |