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Title: On the stationary Boussinesq-Stefan problem with constitutive power-laws
Authors: Rodrigues, José Francisco 
Urbano, José Miguel 
Keywords: free boundary problems; Boussinesq-Stefan problem; non-Newtonian flow; thermomechanics of solidification; p-Laplacian; variational inequalities
Issue Date: 1998
Citation: International Journal of Non-Linear Mechanics. 33:4 (1998) 555-566
Abstract: We discuss the existence of weak solutions to a steady-state coupled system between a two-phase Stefan problem, with convection and non-Fourier heat diffusion, and an elliptic variational inequality traducing the non-Newtonian flow only in the liquid phase. In the Stefan problem for the p-Laplacian equation the main restriction comes from the requirement that the liquid zone is at least an open subset, a fact that leads us to search for a continuous temperature field. Through the heat convection coupling term, this depends on the q-integrability of the velocity gradient and the imbedding theorems of Sobolev. We show that the appropriate condition for the continuity to hold, combining these two powers, is pq> n. This remarkably simple condition, together with q> 3n/(n + 2), that assures the compactness of the convection term, is sufficient to obtain weak solvability results for the interesting space dimension cases n = 2 and n = 3.
DOI: 10.1016/s0020-7462(97)00041-3
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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