A steady-state Boussinesq-Stefan problem with continuous extraction
type: Item
instance of: scholarly article
title: A steady-state Boussinesq-Stefan problem with continuous extraction
zbMATH Open document ID: 0631.35083
DOI: 10.1007/BF01760819
author: José Francisco Rodrigues
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: A model is developed in this paper for the solution of a steady-state Boussinesq-Stefan problem with continuous extraction. For this purpose the equations of the coupled Boussinesq-Stefan system with mixed boundary conditions of the thermal field are presented in their classical form. This procedure is based on the Schauder fixed-point theorem. The existence, uniqueness and continuous dependence of the solution of an auxiliary mixed boundary-value problem for the temperature containing Lipschitz nonlinearities in its divergent term is proved. Finally by letting the extraction velocity to tend zero with the help of appropriate lateral coolings the two-phase Rayleigh-Bénard case with Dirichlet type thermal boundary conditions is derived. The paper follows a well- coordinated, inductive form, making it very readable.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 4026010
zbMATH Keywords: steady-state Boussinesq-Stefan problem
zbMATH Keywords: continuous extraction
zbMATH Keywords: mixed boundary conditions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence
zbMATH Keywords: Lipschitz nonlinearities
zbMATH Keywords: two-phase Rayleigh-Bénard
MaRDI profile type: Publication
cites work: The steady state Stefan problem with convection
cites work: Q3956656
cites work: Natural convection in steady solidification: Finite element analysis of a two-phase Rayleigh-Bénard problem
cites work: On the steady-state continuous casting Stefan problem with nonlinear cooling
cites work: Q4053162
cites work: Elliptic Partial Differential Equations of Second Order
cites work: Q5576913
cites work: Q3722993
cites work: Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni hölderiane
cites work: Q4192429
full work available at URL: https://doi.org/10.1007/bf01760819
OpenAlex ID: W2031853214
description: scientific article; zbMATH DE number 4026010