On the stationary boussinesq-stefan problem with constitutive power-laws

José Francisco Rodrigues, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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. © 1997 Elsevier Science Ltd.
Original languageEnglish (US)
Pages (from-to)555-566
Number of pages12
JournalInternational Journal of Non-Linear Mechanics
Issue number4
StatePublished - Jan 1 1998
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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