Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux. (Strong solutions and asymptotic behaviour for a natural convection problem in porous media)
type: Item
instance of: scholarly article
title: Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux. (Strong solutions and asymptotic behaviour for a natural convection problem in porous media)
zbMATH Open document ID: 0609.76091
DOI: 10.1007/BF00046977
author: Pierre Fabrie
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: Considering the natural convection problem in a porous medium enclosed in an impermeable parallelepipedon with isothermal horizontal faces and adiabatic lateral faces, the author proves by a fixed point method the existence and uniqueness of the strong solutions of the Darcy-Boussinesq equations. We have to mention that, by a different method, the general case has been solved [see the reviewer, On the existence and uniqueness of instationary convection in porous media, An. Stiint. Univ. Al. I. Cuza. Iasi, N. Ser., Sect. Ia 32, No.3, 75-84 (1986)]. In the second part of the article, using a method from the theory of the Navier-Stokes equations, it is proved that the solution is completely determined by its nodal values on a finite set.
reviewed by: Dan Polisevski
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3986926
zbMATH Keywords: natural convection
zbMATH Keywords: porous medium
zbMATH Keywords: impermeable parallelepipedon
zbMATH Keywords: isothermal horizontal faces
zbMATH Keywords: adiabatic lateral faces
zbMATH Keywords: fixed point method
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: strong solutions
zbMATH Keywords: Darcy-Boussinesq equations
zbMATH Keywords: instationary convection
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: nodal values
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00046977
OpenAlex ID: W331814396
description: scientific article; zbMATH DE number 3986926