Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/4667
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. | URI: | https://hdl.handle.net/10316/4667 | DOI: | 10.1016/s0020-7462(97)00041-3 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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file224ec5ad0bd641ad891bab96e7d98e10.pdf | 1.03 MB | Adobe PDF | View/Open |
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